Edit Profile (opens in new tab) Dunster, T. M. Co-Author Distance Author ID: dunster.t-m Published as: Dunster, T. M. Documents Indexed: 53 Publications since 1986, including 4 Additional arXiv Preprints Co-Authors: 11 Co-Authors with 14 Joint Publications 200 Co-Co-Authors all top 5 Co-Authors 39 single-authored 7 Segura, Javier 2 Lutz, Donald A. 2 Temme, Nico M. 1 Boyd, William G. C. 1 Cohl, Howard Saul 1 Dang, Thinh H. 1 Lam, Kim Fung 1 Paris, Richard Bruce 1 Perez, Jessica M. 1 Schäfke, Reinhard 1 Yedlin, Matthew J. all top 5 Serials 9 SIAM Journal on Mathematical Analysis 6 Studies in Applied Mathematics 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Analysis and Applications (Singapore) 4 Methods and Applications of Analysis 3 Journal of Computational and Applied Mathematics 3 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 3 Journal of Classical Analysis 2 Constructive Approximation 1 Computer Physics Communications 1 Journal of Approximation Theory 1 Numerical Algorithms 1 Advances in Computational Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Involve all top 5 Fields 42 Special functions (33-XX) 40 Ordinary differential equations (34-XX) 12 Approximations and expansions (41-XX) 6 Functions of a complex variable (30-XX) 3 Optics, electromagnetic theory (78-XX) 2 Numerical analysis (65-XX) 1 Number theory (11-XX) 1 Partial differential equations (35-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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