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Author ID: dunster.t-m Recent zbMATH articles by "Dunster, T. M."
Published as: Dunster, T. M.

Publications by Year

Citations contained in zbMATH Open

40 Publications have been cited 230 times in 166 Documents Cited by Year
Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. Zbl 0703.33002
Dunster, T. M.
39
1990
Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions. Zbl 0591.34048
Boyd, W. G. C.; Dunster, T. M.
18
1986
Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. Zbl 0673.33003
Dunster, T. M.
16
1989
Uniform asymptotic expansions for Charlier polynomials. Zbl 0991.41020
Dunster, T. M.
13
2001
Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions. Zbl 0798.34083
Dunster, T. M.; Lutz, D. A.; Schäfke, R.
11
1993
Uniform asymptotic expansions for prolate spheroidal functions with large parameters. Zbl 0606.33011
Dunster, T. M.
10
1986
Conical functions with one or both parameters large. Zbl 0736.33002
Dunster, T. M.
9
1991
Computation of asymptotic expansions of turning point problems via Cauchy’s integral formula: Bessel functions. Zbl 1386.34107
Dunster, T. M.; Gil, A.; Segura, J.
8
2017
Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. Zbl 0983.33005
Dunster, T. M.
6
2001
Asymptotics of the eigenvalues of the rotating harmonic oscillator. Zbl 0928.34063
Dunster, T. M.
6
1998
Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point. Zbl 0722.34051
Dunster, T. M.
6
1990
Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Zbl 0877.34011
Dunster, T. M.
6
1996
Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Zbl 0982.33003
Dunster, T. M.
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
Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Zbl 1152.34394
Dunster, T. M.
5
2001
Fundamental solutions and Gegenbauer expansions of Helmholtz operators in Riemannian spaces of constant curvature. Zbl 1406.35106
Cohl, Howard S.; Dang, Thinh H.; Dunster, T. M.
5
2018
Resonance and the late coefficients in the scattered field of a dielectric circular cylinder. Zbl 1124.78004
Dunster, T. M.; Yedlin, Matthew; Lam, Kim
4
2006
Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Zbl 0866.41025
Dunster, T. M.
4
1996
Error analysis in a uniform asymptotic expansion for the generalised exponential integral. Zbl 0870.33002
Dunster, T. M.
4
1997
On the order derivatives of Bessel functions. Zbl 1379.33007
Dunster, T. M.
4
2017
Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions. Zbl 1141.34352
Dunster, T. M.
4
2004
Asymptotic solutions of inhomogeneous differential equations having a turning point. Zbl 1457.34126
Dunster, T. M.
4
2020
Liouville-Green expansions of exponential form, with an application to modified Bessel functions. Zbl 1437.34086
Dunster, T. M.
4
2020
Simplified error bounds for turning point expansions. Zbl 1491.34101
Dunster, T. M.; Gil, A.; Segura, J.
4
2021
Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions. Zbl 1404.33007
Dunster, T. M.; Gil, A.; Segura, J.
4
2018
Quasi-nonuniqueness in the scattered field of a dielectric circular cylinder. Zbl 1188.78004
Dunster, T. M.
3
2010
Uniform asymptotic expansions for associated Legendre functions of large order. Zbl 1055.33008
Dunster, T. M.
3
2003
Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane. Zbl 0798.34062
Dunster, T. M.
3
1994
Uniform asymptotic approximations for incomplete Riemann zeta functions. Zbl 1091.33016
Dunster, T. M.
2
2006
On the logarithmic derivative of Nicholson’s integral. Zbl 1184.33003
Dunster, T. M.
2
2009
Simplified asymptotic solutions of differential equations having two turning points, with an application to Legendre functions. Zbl 1254.34018
Dunster, T. M.
2
2011
Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Zbl 1295.33006
Dunster, T. M.
2
2014
Conical functions of purely imaginary order and argument. Zbl 1307.34090
Dunster, T. M.
2
2013
Uniform asymptotic approximation of Mathieu functions. Zbl 0835.33014
Dunster, T. M.
1
1994
Uniform asymptotic approximations for the Whittaker functions \(M_ {\kappa,i\mu}(z)\) and \(W_{\kappa,i\mu}(z)\). Zbl 1046.33004
Dunster, T. M.
1
2003
Uniform asymptotic expansions for oblate spheroidal functions. I: Positive separation parameter \(\lambda{}\). Zbl 0781.33010
Dunster, T. M.
1
1992
Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one. Zbl 0859.34039
Dunster, T. M.
1
1996
Asymptotics of prolate spheroidal wave functions. Zbl 1424.33035
Dunster, T. M.
1
2017
Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations. Zbl 1513.34357
Dunster, T. M.
1
2020
Nield-Kuznetsov functions and Laplace transforms of parabolic cylinder functions. Zbl 1493.33001
Dunster, T. M.
1
2021
Simplified error bounds for turning point expansions. Zbl 1491.34101
Dunster, T. M.; Gil, A.; Segura, J.
4
2021
Nield-Kuznetsov functions and Laplace transforms of parabolic cylinder functions. Zbl 1493.33001
Dunster, T. M.
1
2021
Asymptotic solutions of inhomogeneous differential equations having a turning point. Zbl 1457.34126
Dunster, T. M.
4
2020
Liouville-Green expansions of exponential form, with an application to modified Bessel functions. Zbl 1437.34086
Dunster, T. M.
4
2020
Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations. Zbl 1513.34357
Dunster, T. M.
1
2020
Fundamental solutions and Gegenbauer expansions of Helmholtz operators in Riemannian spaces of constant curvature. Zbl 1406.35106
Cohl, Howard S.; Dang, Thinh H.; Dunster, T. M.
5
2018
Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions. Zbl 1404.33007
Dunster, T. M.; Gil, A.; Segura, J.
4
2018
Computation of asymptotic expansions of turning point problems via Cauchy’s integral formula: Bessel functions. Zbl 1386.34107
Dunster, T. M.; Gil, A.; Segura, J.
8
2017
On the order derivatives of Bessel functions. Zbl 1379.33007
Dunster, T. M.
4
2017
Asymptotics of prolate spheroidal wave functions. Zbl 1424.33035
Dunster, T. M.
1
2017
Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Zbl 1295.33006
Dunster, T. M.
2
2014
Conical functions of purely imaginary order and argument. Zbl 1307.34090
Dunster, T. M.
2
2013
Simplified asymptotic solutions of differential equations having two turning points, with an application to Legendre functions. Zbl 1254.34018
Dunster, T. M.
2
2011
Quasi-nonuniqueness in the scattered field of a dielectric circular cylinder. Zbl 1188.78004
Dunster, T. M.
3
2010
On the logarithmic derivative of Nicholson’s integral. Zbl 1184.33003
Dunster, T. M.
2
2009
Resonance and the late coefficients in the scattered field of a dielectric circular cylinder. Zbl 1124.78004
Dunster, T. M.; Yedlin, Matthew; Lam, Kim
4
2006
Uniform asymptotic approximations for incomplete Riemann zeta functions. Zbl 1091.33016
Dunster, T. M.
2
2006
Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions. Zbl 1141.34352
Dunster, T. M.
4
2004
Uniform asymptotic expansions for associated Legendre functions of large order. Zbl 1055.33008
Dunster, T. M.
3
2003
Uniform asymptotic approximations for the Whittaker functions \(M_ {\kappa,i\mu}(z)\) and \(W_{\kappa,i\mu}(z)\). Zbl 1046.33004
Dunster, T. M.
1
2003
Uniform asymptotic expansions for Charlier polynomials. Zbl 0991.41020
Dunster, T. M.
13
2001
Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. Zbl 0983.33005
Dunster, T. M.
6
2001
Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Zbl 1152.34394
Dunster, T. M.
5
2001
Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Zbl 0982.33003
Dunster, T. M.
5
1999
Asymptotics of the eigenvalues of the rotating harmonic oscillator. Zbl 0928.34063
Dunster, T. M.
6
1998
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
Error analysis in a uniform asymptotic expansion for the generalised exponential integral. Zbl 0870.33002
Dunster, T. M.
4
1997
Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Zbl 0877.34011
Dunster, T. M.
6
1996
Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Zbl 0866.41025
Dunster, T. M.
4
1996
Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one. Zbl 0859.34039
Dunster, T. M.
1
1996
Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane. Zbl 0798.34062
Dunster, T. M.
3
1994
Uniform asymptotic approximation of Mathieu functions. Zbl 0835.33014
Dunster, T. M.
1
1994
Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions. Zbl 0798.34083
Dunster, T. M.; Lutz, D. A.; Schäfke, R.
11
1993
Uniform asymptotic expansions for oblate spheroidal functions. I: Positive separation parameter \(\lambda{}\). Zbl 0781.33010
Dunster, T. M.
1
1992
Conical functions with one or both parameters large. Zbl 0736.33002
Dunster, T. M.
9
1991
Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. Zbl 0703.33002
Dunster, T. M.
39
1990
Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point. Zbl 0722.34051
Dunster, T. M.
6
1990
Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. Zbl 0673.33003
Dunster, T. M.
16
1989
Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions. Zbl 0591.34048
Boyd, W. G. C.; Dunster, T. M.
18
1986
Uniform asymptotic expansions for prolate spheroidal functions with large parameters. Zbl 0606.33011
Dunster, T. M.
10
1986
all top 5

Cited by 195 Authors

24 Dunster, T. M.
13 Temme, Nico M.
11 Segura, Javier
6 Nemes, Gergő
5 López, José Luis
4 Boyd, John Philip
3 Bremer, James C.
3 Dixit, Atul
3 Dominici, Diego Ernesto
3 Frolenkov, Dmitriĭ Andreevich
3 Long, Wen-Gao
3 Martini, Alessio
3 Wong, Roderick Sue-Chuen
3 Zeng, Zhaoyun
3 Zhao, Yuqiu
2 Balkanova, Ol’ga Germanovna
2 Balser, Werner
2 Bonami, Aline
2 Buttcane, Jack
2 Casarino, Valentina
2 Ciatti, Paolo
2 Cohl, Howard Saul
2 Deaño, Alfredo
2 Fabijonas, Bruce R.
2 Ferreira, Chelo
2 Gautschi, Walter
2 Gil, Amparo
2 González-Santander, Juan Luis
2 Johnstone, Iain Murray
2 Karoui, Abderrazek
2 Kozlov, Vladimir A.
2 Kumar, Rahul
2 Li, Yutian
2 Matveeva, Inessa Izotovna
2 Ndayiragije, François
2 Olde Daalhuis, Adri B.
2 Pérez Sinusía, Ester
2 Van Assche, Walter
1 Aashish, Sandeep
1 Abul-Dahab, Mohamed
1 Abul-ez, M. A.
1 Acharya, Ratnadeep
1 Acho, Thomas Mbah
1 Aiyer, Aditya K.
1 Ajith, Abhijith
1 Akemann, Gernot
1 Andrianov, Alexander A.
1 Arista, Jonas
1 Armendariz-Picon, Cristian
1 Arponen, Heikki
1 Askerov, Idrak M.
1 Bai, Xiao-Xi
1 Bairamov, Elgiz
1 Bakaleinikov, Leonid
1 Barnett, Alex H.
1 Bhat, Pallavi
1 Bieliavsky, Pierre
1 Blaschke, Petr
1 Booker, Andrew R.
1 Bosbach, Christof
1 Brezhnev, Yurii V.
1 Bykovskiĭ, Viktor Alekseevich
1 Chen, Lan
1 Chronik, Blaine A.
1 Cikovic, Milan
1 Clemence, Dominic P.
1 Coffey, Mark William
1 Comets, Francis M.
1 Constales, Denis
1 Costin, Ovidiu
1 Creagh, Stephen C.
1 Dai, Dan
1 Dang, Thinh H.
1 Dasgupta, Anirvan
1 de Goursac, Axel Marcillaud
1 Deglmann, M. L.
1 Demidenko, Gennadiĭ Vladimirovich
1 Demni, Nizar
1 Dimakis, Nikolaos
1 Donninger, Roland
1 Durand, Loyal III
1 Ferreira, Erasmo M.
1 Figari, Rodolfo
1 Fitzgerald, Rosa M.
1 Fukushima, Toshio
1 Gamarnik, David
1 Gassner, Gregor J.
1 Gatteschi, Luigi
1 Gawronski, Wolfgang
1 Getmanenko, Alexander
1 Ghosh, Amit
1 Giacomin, Giambattista
1 Giordano, Carla
1 Goldberg, David Alan
1 Gradoni, Gabriele
1 Greenblatt, Rafael Leon
1 Gryb, Sean
1 Heifetz, Eyal
1 Hirtenstein, Jessie E.
1 Horvai, Peter
...and 95 more Authors
all top 5

Cited in 76 Serials

14 Journal of Computational and Applied Mathematics
10 Analysis and Applications (Singapore)
8 Journal of Mathematical Analysis and Applications
6 Journal of Approximation Theory
6 Studies in Applied Mathematics
5 Communications in Mathematical Physics
5 Journal of Computational Physics
4 Journal of Differential Equations
4 Constructive Approximation
4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
4 Journal of Mathematical Chemistry
3 Journal of Mathematical Physics
3 Mathematics of Computation
3 Numerical Algorithms
3 SIAM Journal on Mathematical Analysis
3 Applied and Computational Harmonic Analysis
3 The Ramanujan Journal
3 Journal of Classical Analysis
3 Research in the Mathematical Sciences
2 Classical and Quantum Gravity
2 Journal of Fluid Mechanics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Advances in Mathematics
2 The Annals of Statistics
2 Applied Mathematics and Computation
2 Mathematika
2 Results in Mathematics
2 Siberian Mathematical Journal
2 Advances in Computational Mathematics
2 Journal of Cosmology and Astroparticle Physics
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Journal of Physics A: Mathematical and Theoretical
2 Algebra & Number Theory
1 Applicable Analysis
1 General Relativity and Gravitation
1 International Journal of Theoretical Physics
1 Journal of Statistical Physics
1 Mathematical Methods in the Applied Sciences
1 Mathematical Notes
1 Physics Letters. B
1 Theoretical and Mathematical Physics
1 Theory of Probability and its Applications
1 BIT
1 Journal of the London Mathematical Society. Second Series
1 Mathematische Nachrichten
1 Nagoya Mathematical Journal
1 Numerische Mathematik
1 Transactions of the American Mathematical Society
1 Physica D
1 Queueing Systems
1 Journal of Scientific Computing
1 Forum Mathematicum
1 The Annals of Applied Probability
1 Geometric and Functional Analysis. GAFA
1 Annals of Physics
1 Indagationes Mathematicae. New Series
1 Russian Journal of Mathematical Physics
1 Sbornik: Mathematics
1 Abstract and Applied Analysis
1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Journal of Interdisciplinary Mathematics
1 European Journal of Mechanics. A. Solids
1 LMS Journal of Computation and Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Journal of High Energy Physics
1 Annales Henri Poincaré
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Computational Methods and Function Theory
1 Central European Journal of Mathematics
1 Boundary Value Problems
1 Waves in Random and Complex Media
1 International Journal of Number Theory
1 Complex Variables and Elliptic Equations
1 Advances in Applied Mathematics and Mechanics
1 Journal of Applied Analysis and Computation
1 Journal of Mathematics
all top 5

Cited in 38 Fields

90 Special functions (33-XX)
48 Ordinary differential equations (34-XX)
34 Approximations and expansions (41-XX)
27 Numerical analysis (65-XX)
17 Number theory (11-XX)
14 Partial differential equations (35-XX)
14 Quantum theory (81-XX)
11 Harmonic analysis on Euclidean spaces (42-XX)
8 Functions of a complex variable (30-XX)
8 Probability theory and stochastic processes (60-XX)
7 Fluid mechanics (76-XX)
7 Relativity and gravitational theory (83-XX)
6 Integral transforms, operational calculus (44-XX)
4 Operator theory (47-XX)
4 Global analysis, analysis on manifolds (58-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Sequences, series, summability (40-XX)
3 Differential geometry (53-XX)
3 Optics, electromagnetic theory (78-XX)
2 Topological groups, Lie groups (22-XX)
2 Real functions (26-XX)
2 Potential theory (31-XX)
2 Difference and functional equations (39-XX)
2 Abstract harmonic analysis (43-XX)
2 Statistics (62-XX)
2 Computer science (68-XX)
2 Mechanics of deformable solids (74-XX)
2 Statistical mechanics, structure of matter (82-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Integral equations (45-XX)
1 Functional analysis (46-XX)
1 Mechanics of particles and systems (70-XX)
1 Astronomy and astrophysics (85-XX)
1 Geophysics (86-XX)
1 Operations research, mathematical programming (90-XX)
1 Systems theory; control (93-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year