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Paris, Richard Bruce

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Author ID: paris.richard-bruce Recent zbMATH articles by "Paris, Richard Bruce"
Published as: Paris, R.; Paris, R. B.; Paris, Richard; Paris, Richard B.; Paris, Richard Bruce; Paris, Rıchard Bruce
Documents Indexed: 127 Publications since 1975, including 3 Books
Reviewing Activity: 76 Reviews
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Serials

22 Journal of Computational and Applied Mathematics
10 Journal of Classical Analysis
7 Integral Transforms and Special Functions
5 Lithuanian Mathematical Journal
5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
5 Applied Mathematical Sciences (Ruse)
4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
4 Methods and Applications of Analysis
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Applied Mathematics and Computation
3 European Journal of Pure and Applied Mathematics
2 Mathematical Methods in the Applied Sciences
2 Physics of Fluids
2 Results in Mathematics
2 Turkish Journal of Mathematics
2 Mathematical Communications
2 Mathematical Inequalities & Applications
2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 Miskolc Mathematical Notes
2 Encyclopedia of Mathematics and Its Applications
1 American Mathematical Monthly
1 Computers & Mathematics with Applications
1 IMA Journal of Applied Mathematics
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Canadian Mathematical Bulletin
1 Philosophical Transactions of the Royal Society of London. Ser. A
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 The Quarterly Journal of Mathematics. Oxford Second Series
1 Applied Mathematics Letters
1 Mathematica Balkanica. New Series
1 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences
1 SIAM Journal on Mathematical Analysis
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Bulletin. The Institute of Mathematics and its Applications
1 Irish Mathematical Society Bulletin
1 Fractional Calculus & Applied Analysis
1 Far East Journal of Mathematical Sciences
1 Advances and Applications in Statistics
1 Hacettepe Journal of Mathematics and Statistics
1 Journal of Mathematical Inequalities
1 Journal of Nonlinear Science and Applications
1 Journal of Statistical Distributions and Applications
1 Journal of Ramanujan Society of Mathematics and Mathematical Sciences

Publications by Year

Citations contained in zbMATH

95 Publications have been cited 604 times in 402 Documents Cited by Year
Asymptotics and Mellin-Barnes integrals. Zbl 0983.41019
Paris, R. B.; Kaminski, D.
117
2001
Extended hypergeometric and confluent hypergeometric functions. Zbl 1067.33001
Chaudhry, M. Aslam; Qadir, Asghar; Srivastava, H. M.; Paris, R. B.
62
2004
Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function. Zbl 1328.33001
Chen, Chao-Ping; Paris, Richard B.
21
2015
Transformation formulas for the generalized hypergeometric function with integral parameter differences. Zbl 1275.33009
Miller, A. R.; Paris, R. B.
18
2013
The asymptotic behaviour of Pearcey’s integral for complex variables. Zbl 0739.33014
Paris, R. B.
17
1991
On the \(L^ 2\) nature of solutions of \(n\)th order symmetric differential equations and McLeod’s conjecture. Zbl 0483.34014
Paris, R. B.; Wood, A. D.
16
1981
Hadamard expansions and hyperasymptotic evaluation. An extension of the method of steepest descents. Zbl 1223.41021
Paris, R. B.
15
2011
Asymptotics of high order differential equations. Zbl 0644.34052
Paris, R. B.; Wood, A. D.
15
1986
A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function. Zbl 1062.33008
Paris, R. B.
14
2005
Extended Riemann-Liouville fractional derivative operator and its applications. Zbl 1329.26010
Agarwal, Praveen; Choi, Junesang; Paris, R. B.
12
2015
Exponentially small expansions in the asymptotics of the Wright function. Zbl 1215.33003
Paris, R. B.
11
2010
Exponential asymptotics of the Mittag-Leffler function. Zbl 1049.33018
Paris, R. B.
11
2002
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: Real variable. Zbl 1052.41016
Paris, R. B.
10
2004
Certain transformations and summations for generalized hypergeometric series with integral parameter differences. Zbl 1217.33013
Miller, A. R.; Paris, R. B.
9
2011
Exactification of the method of steepest descents: the Bessel functions of large order and argument. Zbl 1071.65024
Paris, R. B.
9
2004
Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\). Zbl 1225.33005
Miller, A. R.; Paris, R. B.
8
2011
Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions. Zbl 1086.65012
Paris, R. B.; Kaminski, D.
8
2006
On a result related to transformations and summations of generalized hypergeometric series. Zbl 1248.33012
Miller, Allen Richard; Paris, Richard Bruce
7
2012
Smoothing of the Stokes phenomenon for high-order differential equations. Zbl 0748.34008
Paris, R. B.
7
1992
New properties and representations for members of the power-variance family. II. Zbl 1277.60036
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
6
2013
New properties and representations for members of the power-variance family. I. Zbl 1284.60040
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
6
2012
Clausen’s series \(_{3} F _{2}(1)\) with integral parameter differences and transformations of the hypergeometric function \(_{2} F _{2}(x)\). Zbl 1258.33004
Miller, A. R.; Paris, R. B.
6
2012
Exponentially-improved asymptotics for the gamma function. Zbl 0755.33001
Paris, R. B.; Wood, A. D.
6
1992
Exponentially small expansions of the Wright function on the Stokes lines. Zbl 1306.33014
Paris, Richard B.
5
2014
On two Thomae-type transformations for hypergeometric series with integral parameter differences. Zbl 1295.33010
Kim, Yong Sup; Rathie, Arjun K.; Paris, Richard Bruce
5
2014
Asymptotics of the Gauss hypergeometric function with large parameters. II. Zbl 1412.33009
Paris, R. B.
5
2013
An extension of Saalschütz’s summation theorem for the series \(_{r+3}F_{r+2}\). Zbl 1286.33006
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
5
2013
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. II: Complex variable. Zbl 1052.41017
Paris, R. B.
5
2004
On the asymptotic connection between two exponential sums. Zbl 1162.11370
Paris, R. B.
5
2003
A uniform asymptotic expansion for the incomplete gamma function. Zbl 1013.33002
Paris, R. B.
5
2002
Error bounds for the uniform asymptotic expansion of the incomplete gamma function. Zbl 1013.65016
Paris, R. B.
5
2002
On the use of Hadamard expansions in hyperasymptotic evaluation. I: Real variables. Zbl 1039.33500
Paris, R. B.
5
2001
On the use of Hadamard expansions in hyperasymptotic evaluation. II: Complex variables. Zbl 1097.33503
Paris, R. B.
5
2001
On the zeros of the Pearcey integral. Zbl 0931.41018
Kaminski, D.; Paris, R. B.
5
1999
On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function. Zbl 0921.33001
Dunster, T. M.; Paris, R. B.; Cang, S.
5
1998
An asymptotic representation for \(\zeta(\frac{1}{2}+it)\). Zbl 0913.11033
Paris, R. B.; Cang, S.
5
1997
Smoothing of the Stokes phenomenon using Mellin-Barnes integrals. Zbl 0772.33015
Paris, R. B.
5
1992
Asymptotics of the Gauss hypergeometric function with large parameters. I. Zbl 1412.33008
Paris, R. B.
4
2013
Asymptotic approximations for \(n\)! Zbl 1242.41034
Paris, R. B.
4
2011
The asymptotics of the generalised Hermite-Bell polynomials. Zbl 1176.33014
Paris, R. B.
4
2009
An asymptotic approximation for incomplete Gauss sums. II. Zbl 1194.11085
Paris, R. B.
4
2008
An asymptotic approximation for incomplete Gauss sums. Zbl 1099.11041
Paris, R. B.
4
2005
Asymptotics of a class of multidimensional Laplace-type integrals. II: Treble integrals. Zbl 0905.41018
Kaminski, D.; Paris, R. B.
4
1998
Asymptotics of a class of multidimensional Laplace-type integrals. I: Double integrals. Zbl 0905.41017
Kaminski, D.; Paris, R. B.
4
1998
Stokes phenomenon demystified. Zbl 0827.34002
Paris, R. B.; Wood, A. D.
4
1995
On the asymptotic expansions of solutions of an \(n\)th order linear differential equation. Zbl 0429.34010
Paris, R. B.
4
1980
Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities. I. Zbl 1441.11034
Chen, Chao-Ping; Paris, Richard B.
3
2017
Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences. Zbl 1412.33013
Rathie, Arjun K.; Paris, R. B.
3
2013
High-precision evaluation of the Bessel functions via Hadamard series. Zbl 1157.65020
Paris, R. B.
3
2009
An asymptotic expansion for the generalised quadratic Gauss sum. Zbl 1154.11023
Paris, R. B.
3
2008
An extension of the Euler-type transformation for the \(_3F_2\) series. Zbl 1151.33006
Rathie, A. K.; Paris, R. B.
3
2007
An asymptotic representation for the Riemann zeta function on the critical line. Zbl 0827.11051
Paris, R. B.
3
1994
The eigenvalues of the simplified ideal MHD ballooning equation. Zbl 0599.76055
Paris, R. B.; Auby, N.; Dagazian, R. Y.
3
1986
The asymptotic expansion of solutions of the differential equation \(u^{iv}+\lambda^2[(z^2+c)''+azu'+bu]=0\) for large \(| z|\). Zbl 0431.34040
Paris, R. B.; Wood, A. D.
3
1980
On an extension of extended beta and hypergeometric functions. Zbl 1424.33008
Parmar, Rakesh K.; Chopra, Purnima; Paris, Richard B.
2
2017
Asymptotic and structural properties of special cases of the Wright function arising in probability theory. Zbl 1360.33012
Paris, Richard B.; Vinogradov, Vladimir
2
2016
Generalizations of two infinite product formulas. Zbl 1303.33001
Chen, Chao-Ping; Paris, Richard B.
2
2014
Generalization of two theorems due to Ramanujan. Zbl 1277.33005
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
2
2013
A generalised Kummer-type transformation for the \(_pF_p(x)\) hypergeometric function. Zbl 1314.33006
Miller, A. R.; Paris, R. B.
2
2012
On a new class of summation formulae involving the Laguerre polynomial. Zbl 1273.33010
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
2
2012
The discrete analogue of Laplace’s method. Zbl 1222.41043
Paris, R. B.
2
2011
Asymptotics of integrals of Hermite polynomials. Zbl 1226.33005
Paris, R. B.
2
2010
A new proof of Watson’s theorem for the series \(_3F_2(1)\). Zbl 1163.33304
Rathie, Arjun K.; Paris, R. B.
2
2009
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. III: Clusters of saddle points. Zbl 1119.41031
Paris, R. B.
2
2007
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. IV: Poles. Zbl 1119.41030
Paris, R. B.
2
2007
Hadamard expansions for integrals with saddles coalescing with an endpoint. Zbl 1089.41028
Paris, R. B.; Kaminski, D.
2
2005
On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type. Zbl 1067.33004
Kaminski, D.; Paris, R. B.
2
2004
Asymptotic expansions of Laplace-type integrals. III. Zbl 0990.41019
Liakhovetski, G. V.; Paris, R. B.
2
2001
Asymptotics of the multidimensional Faxén integral. Zbl 1036.41019
Paris, R. B.; Liakhovetski, G. V.
2
2000
New asymptotic formulas for the Riemann zeta function on the critical line. Zbl 1161.11377
Paris, R. B.
2
2000
Asymptotics via iterated Mellin-Barnes integrals: Application to the generalised Faxén integral. Zbl 0920.41018
Kaminski, D.; Paris, R. B.
2
1997
A model equation for optical tunnelling. Zbl 0695.34057
Paris, R. B.; Wood, A. D.
2
1989
Results old and new on the hyper-Bessel equation. Zbl 0631.34035
Paris, R. B.; Wood, A. D.
2
1987
On the asymptotic expansions of solutions of an \(n\)th order linear differential equation with power coefficients. Zbl 0605.34049
Paris, R. B.; Wood, A. D.
2
1985
Deficiency indices of an odd-order differential operator. Zbl 0574.34037
Paris, R. B.; Wood, A. D.
2
1984
On a generalisation of a result of Ramanujan connected with the exponential series. Zbl 0463.33004
Paris, R. B.
2
1981
Evaluations of some terminating hypergeometric \(_2F_1(2)\) series with applications. Zbl 1424.33015
Kim, Yong Sup; Rathie, Arjunkumar; Paris, Richard Bruce
1
2018
On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas. Zbl 1411.33001
Chen, Chao-Ping; Paris, Richard B.
1
2017
On the asymptotics of products related to generalizations of the Wilf and Mortini problems. Zbl 1350.33001
Chen, Chao-Ping; Paris, Richard B.
1
2016
An alternative proof of the extended Saalschütz summation theorem for the \(_{r + 3}F_{r + 2}(1)\) series with applications. Zbl 1347.33015
Kim, Yong S.; Rathie, Arjun. K.; Paris, Richard B.
1
2015
An asymptotic expansion for the generalised quadratic Gauss sum revisited. Zbl 1412.11086
Paris, R. B.
1
2014
A note on some summations due to Ramanujan, their generalization and some allied series. Zbl 06755910
Rathie, A. K.; Paris, R. B.
1
2014
Erratum to: “New properties and representations for members of the power-variance family. II”. Zbl 1315.60026
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
1
2014
Asymptotic expansion of \(n\)-dimensional Faxén-type integrals. Zbl 1213.30073
Paris, Richard Bruce
1
2010
A generalisation of an expansion for the Riemann zeta function involving incomplete gamma functions. Zbl 1203.11058
Paris, R. B.
1
2009
The asymptotics of a new exponential sum. Zbl 1241.11097
Paris, R. B.
1
2009
The Stokes phenomenon associated with the Hurwitz zeta function \(\zeta (s,a)\). Zbl 1145.11326
Paris, R. B.
1
2005
The asymptotic expansion of a generalised incomplete gamma function. Zbl 1041.33002
Paris, R. B.
1
2003
The asymptotic expansion of Gordeyev’s integral. Zbl 0905.41019
Paris, R. B.
1
1998
An exponentially-smoothed Gram-type formula for the Riemann zeta function. Zbl 0957.11057
Paris, R. B.; Cang, S.
1
1997
A generalization of Pearcey’s integral. Zbl 0799.41031
Paris, R. B.
1
1994
An asymptotic approximation connected with the golden number. Zbl 0627.40003
Paris, R. B.
1
1987
Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability. Zbl 0528.76120
Paris, R. B.; Sy, W. N-C.
1
1983
On a fourth order symmetric differential equation. Zbl 0448.34042
Paris, R. B.; Wood, A. D.
1
1982
The asymptotic behaviour of solutions of the differential equation \({d^4u\over dz^4}+[z^2{d^2u\over dz^2}+az{du\over dz}+bu]=0\). Zbl 0325.34050
Paris, R. B.
1
1975
Evaluations of some terminating hypergeometric \(_2F_1(2)\) series with applications. Zbl 1424.33015
Kim, Yong Sup; Rathie, Arjunkumar; Paris, Richard Bruce
1
2018
Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities. I. Zbl 1441.11034
Chen, Chao-Ping; Paris, Richard B.
3
2017
On an extension of extended beta and hypergeometric functions. Zbl 1424.33008
Parmar, Rakesh K.; Chopra, Purnima; Paris, Richard B.
2
2017
On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas. Zbl 1411.33001
Chen, Chao-Ping; Paris, Richard B.
1
2017
Asymptotic and structural properties of special cases of the Wright function arising in probability theory. Zbl 1360.33012
Paris, Richard B.; Vinogradov, Vladimir
2
2016
On the asymptotics of products related to generalizations of the Wilf and Mortini problems. Zbl 1350.33001
Chen, Chao-Ping; Paris, Richard B.
1
2016
Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function. Zbl 1328.33001
Chen, Chao-Ping; Paris, Richard B.
21
2015
Extended Riemann-Liouville fractional derivative operator and its applications. Zbl 1329.26010
Agarwal, Praveen; Choi, Junesang; Paris, R. B.
12
2015
An alternative proof of the extended Saalschütz summation theorem for the \(_{r + 3}F_{r + 2}(1)\) series with applications. Zbl 1347.33015
Kim, Yong S.; Rathie, Arjun. K.; Paris, Richard B.
1
2015
Exponentially small expansions of the Wright function on the Stokes lines. Zbl 1306.33014
Paris, Richard B.
5
2014
On two Thomae-type transformations for hypergeometric series with integral parameter differences. Zbl 1295.33010
Kim, Yong Sup; Rathie, Arjun K.; Paris, Richard Bruce
5
2014
Generalizations of two infinite product formulas. Zbl 1303.33001
Chen, Chao-Ping; Paris, Richard B.
2
2014
An asymptotic expansion for the generalised quadratic Gauss sum revisited. Zbl 1412.11086
Paris, R. B.
1
2014
A note on some summations due to Ramanujan, their generalization and some allied series. Zbl 06755910
Rathie, A. K.; Paris, R. B.
1
2014
Erratum to: “New properties and representations for members of the power-variance family. II”. Zbl 1315.60026
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
1
2014
Transformation formulas for the generalized hypergeometric function with integral parameter differences. Zbl 1275.33009
Miller, A. R.; Paris, R. B.
18
2013
New properties and representations for members of the power-variance family. II. Zbl 1277.60036
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
6
2013
Asymptotics of the Gauss hypergeometric function with large parameters. II. Zbl 1412.33009
Paris, R. B.
5
2013
An extension of Saalschütz’s summation theorem for the series \(_{r+3}F_{r+2}\). Zbl 1286.33006
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
5
2013
Asymptotics of the Gauss hypergeometric function with large parameters. I. Zbl 1412.33008
Paris, R. B.
4
2013
Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences. Zbl 1412.33013
Rathie, Arjun K.; Paris, R. B.
3
2013
Generalization of two theorems due to Ramanujan. Zbl 1277.33005
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
2
2013
On a result related to transformations and summations of generalized hypergeometric series. Zbl 1248.33012
Miller, Allen Richard; Paris, Richard Bruce
7
2012
New properties and representations for members of the power-variance family. I. Zbl 1284.60040
Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga
6
2012
Clausen’s series \(_{3} F _{2}(1)\) with integral parameter differences and transformations of the hypergeometric function \(_{2} F _{2}(x)\). Zbl 1258.33004
Miller, A. R.; Paris, R. B.
6
2012
A generalised Kummer-type transformation for the \(_pF_p(x)\) hypergeometric function. Zbl 1314.33006
Miller, A. R.; Paris, R. B.
2
2012
On a new class of summation formulae involving the Laguerre polynomial. Zbl 1273.33010
Kim, Y. S.; Rathie, A. K.; Paris, R. B.
2
2012
Hadamard expansions and hyperasymptotic evaluation. An extension of the method of steepest descents. Zbl 1223.41021
Paris, R. B.
15
2011
Certain transformations and summations for generalized hypergeometric series with integral parameter differences. Zbl 1217.33013
Miller, A. R.; Paris, R. B.
9
2011
Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\). Zbl 1225.33005
Miller, A. R.; Paris, R. B.
8
2011
Asymptotic approximations for \(n\)! Zbl 1242.41034
Paris, R. B.
4
2011
The discrete analogue of Laplace’s method. Zbl 1222.41043
Paris, R. B.
2
2011
Exponentially small expansions in the asymptotics of the Wright function. Zbl 1215.33003
Paris, R. B.
11
2010
Asymptotics of integrals of Hermite polynomials. Zbl 1226.33005
Paris, R. B.
2
2010
Asymptotic expansion of \(n\)-dimensional Faxén-type integrals. Zbl 1213.30073
Paris, Richard Bruce
1
2010
The asymptotics of the generalised Hermite-Bell polynomials. Zbl 1176.33014
Paris, R. B.
4
2009
High-precision evaluation of the Bessel functions via Hadamard series. Zbl 1157.65020
Paris, R. B.
3
2009
A new proof of Watson’s theorem for the series \(_3F_2(1)\). Zbl 1163.33304
Rathie, Arjun K.; Paris, R. B.
2
2009
A generalisation of an expansion for the Riemann zeta function involving incomplete gamma functions. Zbl 1203.11058
Paris, R. B.
1
2009
The asymptotics of a new exponential sum. Zbl 1241.11097
Paris, R. B.
1
2009
An asymptotic approximation for incomplete Gauss sums. II. Zbl 1194.11085
Paris, R. B.
4
2008
An asymptotic expansion for the generalised quadratic Gauss sum. Zbl 1154.11023
Paris, R. B.
3
2008
An extension of the Euler-type transformation for the \(_3F_2\) series. Zbl 1151.33006
Rathie, A. K.; Paris, R. B.
3
2007
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. III: Clusters of saddle points. Zbl 1119.41031
Paris, R. B.
2
2007
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. IV: Poles. Zbl 1119.41030
Paris, R. B.
2
2007
Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions. Zbl 1086.65012
Paris, R. B.; Kaminski, D.
8
2006
A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function. Zbl 1062.33008
Paris, R. B.
14
2005
An asymptotic approximation for incomplete Gauss sums. Zbl 1099.11041
Paris, R. B.
4
2005
Hadamard expansions for integrals with saddles coalescing with an endpoint. Zbl 1089.41028
Paris, R. B.; Kaminski, D.
2
2005
The Stokes phenomenon associated with the Hurwitz zeta function \(\zeta (s,a)\). Zbl 1145.11326
Paris, R. B.
1
2005
Extended hypergeometric and confluent hypergeometric functions. Zbl 1067.33001
Chaudhry, M. Aslam; Qadir, Asghar; Srivastava, H. M.; Paris, R. B.
62
2004
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: Real variable. Zbl 1052.41016
Paris, R. B.
10
2004
Exactification of the method of steepest descents: the Bessel functions of large order and argument. Zbl 1071.65024
Paris, R. B.
9
2004
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. II: Complex variable. Zbl 1052.41017
Paris, R. B.
5
2004
On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type. Zbl 1067.33004
Kaminski, D.; Paris, R. B.
2
2004
On the asymptotic connection between two exponential sums. Zbl 1162.11370
Paris, R. B.
5
2003
The asymptotic expansion of a generalised incomplete gamma function. Zbl 1041.33002
Paris, R. B.
1
2003
Exponential asymptotics of the Mittag-Leffler function. Zbl 1049.33018
Paris, R. B.
11
2002
A uniform asymptotic expansion for the incomplete gamma function. Zbl 1013.33002
Paris, R. B.
5
2002
Error bounds for the uniform asymptotic expansion of the incomplete gamma function. Zbl 1013.65016
Paris, R. B.
5
2002
Asymptotics and Mellin-Barnes integrals. Zbl 0983.41019
Paris, R. B.; Kaminski, D.
117
2001
On the use of Hadamard expansions in hyperasymptotic evaluation. I: Real variables. Zbl 1039.33500
Paris, R. B.
5
2001
On the use of Hadamard expansions in hyperasymptotic evaluation. II: Complex variables. Zbl 1097.33503
Paris, R. B.
5
2001
Asymptotic expansions of Laplace-type integrals. III. Zbl 0990.41019
Liakhovetski, G. V.; Paris, R. B.
2
2001
Asymptotics of the multidimensional Faxén integral. Zbl 1036.41019
Paris, R. B.; Liakhovetski, G. V.
2
2000
New asymptotic formulas for the Riemann zeta function on the critical line. Zbl 1161.11377
Paris, R. B.
2
2000
On the zeros of the Pearcey integral. Zbl 0931.41018
Kaminski, D.; Paris, R. B.
5
1999
On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function. Zbl 0921.33001
Dunster, T. M.; Paris, R. B.; Cang, S.
5
1998
Asymptotics of a class of multidimensional Laplace-type integrals. II: Treble integrals. Zbl 0905.41018
Kaminski, D.; Paris, R. B.
4
1998
Asymptotics of a class of multidimensional Laplace-type integrals. I: Double integrals. Zbl 0905.41017
Kaminski, D.; Paris, R. B.
4
1998
The asymptotic expansion of Gordeyev’s integral. Zbl 0905.41019
Paris, R. B.
1
1998
An asymptotic representation for \(\zeta(\frac{1}{2}+it)\). Zbl 0913.11033
Paris, R. B.; Cang, S.
5
1997
Asymptotics via iterated Mellin-Barnes integrals: Application to the generalised Faxén integral. Zbl 0920.41018
Kaminski, D.; Paris, R. B.
2
1997
An exponentially-smoothed Gram-type formula for the Riemann zeta function. Zbl 0957.11057
Paris, R. B.; Cang, S.
1
1997
Stokes phenomenon demystified. Zbl 0827.34002
Paris, R. B.; Wood, A. D.
4
1995
An asymptotic representation for the Riemann zeta function on the critical line. Zbl 0827.11051
Paris, R. B.
3
1994
A generalization of Pearcey’s integral. Zbl 0799.41031
Paris, R. B.
1
1994
Smoothing of the Stokes phenomenon for high-order differential equations. Zbl 0748.34008
Paris, R. B.
7
1992
Exponentially-improved asymptotics for the gamma function. Zbl 0755.33001
Paris, R. B.; Wood, A. D.
6
1992
Smoothing of the Stokes phenomenon using Mellin-Barnes integrals. Zbl 0772.33015
Paris, R. B.
5
1992
The asymptotic behaviour of Pearcey’s integral for complex variables. Zbl 0739.33014
Paris, R. B.
17
1991
A model equation for optical tunnelling. Zbl 0695.34057
Paris, R. B.; Wood, A. D.
2
1989
Results old and new on the hyper-Bessel equation. Zbl 0631.34035
Paris, R. B.; Wood, A. D.
2
1987
An asymptotic approximation connected with the golden number. Zbl 0627.40003
Paris, R. B.
1
1987
Asymptotics of high order differential equations. Zbl 0644.34052
Paris, R. B.; Wood, A. D.
15
1986
The eigenvalues of the simplified ideal MHD ballooning equation. Zbl 0599.76055
Paris, R. B.; Auby, N.; Dagazian, R. Y.
3
1986
On the asymptotic expansions of solutions of an \(n\)th order linear differential equation with power coefficients. Zbl 0605.34049
Paris, R. B.; Wood, A. D.
2
1985
Deficiency indices of an odd-order differential operator. Zbl 0574.34037
Paris, R. B.; Wood, A. D.
2
1984
Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability. Zbl 0528.76120
Paris, R. B.; Sy, W. N-C.
1
1983
On a fourth order symmetric differential equation. Zbl 0448.34042
Paris, R. B.; Wood, A. D.
1
1982
On the \(L^ 2\) nature of solutions of \(n\)th order symmetric differential equations and McLeod’s conjecture. Zbl 0483.34014
Paris, R. B.; Wood, A. D.
16
1981
On a generalisation of a result of Ramanujan connected with the exponential series. Zbl 0463.33004
Paris, R. B.
2
1981
On the asymptotic expansions of solutions of an \(n\)th order linear differential equation. Zbl 0429.34010
Paris, R. B.
4
1980
The asymptotic expansion of solutions of the differential equation \(u^{iv}+\lambda^2[(z^2+c)''+azu'+bu]=0\) for large \(| z|\). Zbl 0431.34040
Paris, R. B.; Wood, A. D.
3
1980
The asymptotic behaviour of solutions of the differential equation \({d^4u\over dz^4}+[z^2{d^2u\over dz^2}+az{du\over dz}+bu]=0\). Zbl 0325.34050
Paris, R. B.
1
1975
all top 5

Cited by 491 Authors

53 Paris, Richard Bruce
16 Chen, Chaoping
13 Parmar, Rakesh Kumar
12 Agarwal, Praveen
10 Karp, Dmitriĭ Borisovich
10 López, José Luis
10 Rahman, Gauhar
10 Rathie, Arjun Kumar
9 Nemes, Gergő
9 Prilepkina, Elena Gumarovna
9 Srivastava, Hari Mohan
9 Yang, Zhenhang
8 Choi, Junesang
8 Dixit, Atul
8 Mainardi, Francesco
8 Mubeen, Shahid
8 Sooppy Nisar, Kottakkaran
8 Wood, Alastair D.
7 Kim, Yong Sup
6 Tian, Jingfeng
5 Olde Daalhuis, Adri B.
5 Pagola, Pedro J.
5 Pérez Sinusía, Ester
5 Roy, Arindam
5 Vinogradov, Vladimir V.
5 Zaharescu, Alexandru
4 Chaudhry, Muhammad Aslam
4 Dong, Jianping
4 Ferreira, Chelo
4 Garrappa, Roberto
4 Khan, Nabiullah U.
4 Luo, Minjie
4 Miller, Allen Richard
4 Pagnini, Gianni
4 Patie, Pierre
4 Qadir, Asghar
3 Arshad, Muhammad Junaid
3 Arshad, Muhammad Sarmad
3 Băleanu, Dumitru I.
3 Bartušek, Miroslav
3 Boyd, John Philip
3 Çetinkaya, Ayşegül
3 Chand, Mehar
3 Chopra, Purnima
3 Chu, Wenchang
3 Došlá, Zuzana
3 Dunster, T. M.
3 Graef, John R.
3 Kamiński, Dominik
3 Kıymaz, İ. Onur
3 Milgram, Michael S.
3 Nakano, Minoru
3 Ozarslan, Mehmet Ali
3 Pogány, Tibor K.
3 Purohit, Sunil Dutt
3 Rakha, Medhat Ahmed
3 Schultze, Bernd
3 Tomovski, Živorad
3 Usman, Talha
3 Wang, Weiping
3 Yanushkevichiene, Olga
2 Ahmad, Moin
2 Akarsu, Emek Demirci
2 Alqurashi, Maysaa M.
2 Aman, Mohd
2 Blagouchine, Iaroslav V.
2 Blümlein, Johannes
2 Bommier-Hato, Hélène
2 Borwein, Jonathan Michael
2 Chu, Yuming
2 Dar, Showkat Ahmad
2 Eckstein, Michał
2 Elezović, Neven
2 Fan, Engui
2 Gerhold, Stefan
2 Ghaffar, Abdul
2 Jain, Silpi
2 Kanemitsu, Shigeru
2 Khan, Waseem Ahmad
2 Kowalenko, Victor
2 Krefl, Daniel
2 Lin, Long
2 Liu, Hongmei
2 Maier, Robert S.
2 Mirzoev, Karakhan Agakhan
2 Miyamoto, Tadashi
2 Moll, Victor Hugo
2 Mondal, Saiful Rahman
2 Özergin, Emine
2 Polito, Federico
2 Qureshi, Muhammad Imran
2 Raina, Ravinder Krishna
2 Robles, Nicolas
2 Saxena, Ram Kishore
2 Srivastava, Rekha
2 Tassaddiq, Asifa
2 Temme, Nico M.
2 Tsukada, Haruo
2 Valdinoci, Enrico
2 Zhang, Wen
...and 391 more Authors
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Cited in 160 Serials

37 Journal of Computational and Applied Mathematics
19 Applied Mathematics and Computation
18 Journal of Mathematical Analysis and Applications
10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
10 Integral Transforms and Special Functions
9 Journal of Mathematical Physics
8 Advances in Difference Equations
7 Mathematics of Computation
7 Journal of Number Theory
7 Journal of Inequalities and Applications
6 Lithuanian Mathematical Journal
6 The Ramanujan Journal
6 Fractional Calculus & Applied Analysis
6 Journal of High Energy Physics
6 Journal of Classical Analysis
5 Results in Mathematics
5 Communications of the Korean Mathematical Society
4 Communications in Mathematical Physics
4 Mathematical Notes
4 Kyungpook Mathematical Journal
4 Turkish Journal of Mathematics
4 Abstract and Applied Analysis
4 Analysis and Applications (Singapore)
4 Boletim da Sociedade Paranaense de Matemática. Terceira Série
4 Journal of Nonlinear Science and Applications
3 Computers & Mathematics with Applications
3 Journal of Computational Physics
3 Journal of Statistical Physics
3 Mathematical Methods in the Applied Sciences
3 Nuclear Physics. B
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 International Journal of Mathematics and Mathematical Sciences
3 Proceedings of the American Mathematical Society
3 Tokyo Journal of Mathematics
3 Advances in Applied Mathematics
3 Methodology and Computing in Applied Probability
3 Journal of Physics A: Mathematical and Theoretical
3 Journal of Mathematical Inequalities
3 Open Mathematics
2 Rocky Mountain Journal of Mathematics
2 Advances in Mathematics
2 Annals of the Institute of Statistical Mathematics
2 The Annals of Probability
2 The Annals of Statistics
2 Journal of Approximation Theory
2 Journal of Differential Equations
2 Journal of Functional Analysis
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Studies in Applied Mathematics
2 Transactions of the American Mathematical Society
2 Statistics & Probability Letters
2 Constructive Approximation
2 Numerical Algorithms
2 Expositiones Mathematicae
2 Russian Journal of Mathematical Physics
2 Journal of Mathematical Sciences (New York)
2 Boletín de la Sociedad Matemática Mexicana. Third Series
2 Journal of Applied Analysis
2 Mathematical Inequalities & Applications
2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 Communications in Nonlinear Science and Numerical Simulation
2 Integers
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Computational Methods and Function Theory
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Applications and Applied Mathematics
2 European Journal of Pure and Applied Mathematics
2 Journal of Pseudo-Differential Operators and Applications
2 Palestine Journal of Mathematics
2 Journal of Mathematics
1 Acta Mechanica
1 American Mathematical Monthly
1 Applicable Analysis
1 International Journal of Theoretical Physics
1 Journal of Engineering Mathematics
1 Journal of Mathematical Biology
1 Letters in Mathematical Physics
1 Physica A
1 Physics Letters. A
1 Chaos, Solitons and Fractals
1 Duke Mathematical Journal
1 Functiones et Approximatio. Commentarii Mathematici
1 Journal of Economic Theory
1 Kodai Mathematical Journal
1 Manuscripta Mathematica
1 Mathematische Annalen
1 Mathematische Nachrichten
1 Mathematica Scandinavica
1 Mathematika
1 Numerische Mathematik
1 Proceedings of the Japan Academy. Series A
1 Quaestiones Mathematicae
1 Tamkang Journal of Mathematics
1 Theoretical Computer Science
1 Bulletin of the Korean Mathematical Society
1 Applied Mathematics and Mechanics. (English Edition)
1 Applied Numerical Mathematics
1 Journal of Symbolic Computation
1 Probability Theory and Related Fields
1 Statistical Science
...and 60 more Serials
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Cited in 46 Fields

231 Special functions (33-XX)
73 Approximations and expansions (41-XX)
67 Real functions (26-XX)
60 Ordinary differential equations (34-XX)
56 Number theory (11-XX)
36 Probability theory and stochastic processes (60-XX)
26 Quantum theory (81-XX)
24 Functions of a complex variable (30-XX)
20 Numerical analysis (65-XX)
19 Partial differential equations (35-XX)
19 Operator theory (47-XX)
17 Statistics (62-XX)
14 Integral transforms, operational calculus (44-XX)
11 Statistical mechanics, structure of matter (82-XX)
10 Harmonic analysis on Euclidean spaces (42-XX)
9 Combinatorics (05-XX)
9 Dynamical systems and ergodic theory (37-XX)
8 Linear and multilinear algebra; matrix theory (15-XX)
8 Sequences, series, summability (40-XX)
7 Global analysis, analysis on manifolds (58-XX)
5 Difference and functional equations (39-XX)
5 Integral equations (45-XX)
5 Fluid mechanics (76-XX)
5 Optics, electromagnetic theory (78-XX)
5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Functional analysis (46-XX)
4 Relativity and gravitational theory (83-XX)
3 Differential geometry (53-XX)
3 Computer science (68-XX)
3 Mechanics of deformable solids (74-XX)
3 Biology and other natural sciences (92-XX)
2 History and biography (01-XX)
2 Algebraic geometry (14-XX)
2 Nonassociative rings and algebras (17-XX)
2 Topological groups, Lie groups (22-XX)
2 Potential theory (31-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Mechanics of particles and systems (70-XX)
1 Category theory; homological algebra (18-XX)
1 Group theory and generalizations (20-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Abstract harmonic analysis (43-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Astronomy and astrophysics (85-XX)
1 Geophysics (86-XX)
1 Operations research, mathematical programming (90-XX)

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