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pro vyhledávání: '"T. M. Dunster"'
Autor:
T. M. Dunster
Publikováno v:
Studies in Applied Mathematics. 148:340-372
Using a differential equation approach asymptotic expansions are rigorously obtained for Lommel, Weber, Anger-Weber and Struve functions, as well as Neumann polynomials, each of which is a solution of an inhomogeneous Bessel equation. The approximati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c0fb084a8292af0afd6ede709574db06
https://doi.org/10.1111/sapm.12442
https://doi.org/10.1111/sapm.12442
Autor:
T. M. Dunster
Publikováno v:
Studies in Applied Mathematics. 145:500-536
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic appro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61c99aa676b5575c8e9740d51b5deb20
https://doi.org/10.1111/sapm.12326
https://doi.org/10.1111/sapm.12326
Autor:
T. M. Dunster
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros are located.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f98168e9e7a49bd13e156019eb3135a4
Publikováno v:
Computational and Mathematical Methods 2021, 3, 6, e1198
21th International Conference Computational and Mathematical Methods in Science and Engineering (CMMSE 2021)
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
21th International Conference Computational and Mathematical Methods in Science and Engineering (CMMSE 2021)
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
It is well known that one of the most relevant applications of the reverse Bessel polynomials 𝜃�n(z) is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros of 𝜃�n(z). In this article w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ed80dd6dd0fdee591fea9bf64a20327
http://hdl.handle.net/10902/23903
http://hdl.handle.net/10902/23903
Autor:
T. M. Dunster
Publikováno v:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 477
Uniform asymptotic expansions are derived for Whittaker’s confluent hypergeometric functions M κ , μ ( z ) and W κ , μ ( z ) , as well as the numerically satisfactory companion function W − κ , μ ( z e − π i ) . The expansions are unifor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d3756c655d227f6e92865a8e083b51d
https://doi.org/10.1098/rspa.2021.0360
https://doi.org/10.1098/rspa.2021.0360
Publikováno v:
Journal of classical analysis Volume 18, Number 1 (2021), 49-81
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the bounds is il
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fbe29a9265d8f3378395cea2de5f3cdc
http://hdl.handle.net/10902/22760
http://hdl.handle.net/10902/22760
Autor:
T. M. Dunster
Nield-Kuznetsov functions of the first kind are studied, which are solutions of an inhomogeneous parabolic Weber equation, and have applications in fluid flow problems. Connection formulas are constructed between them, numerically satisfactory soluti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c80f8b43d1b08e37da36583a5f6a1eb2
Autor:
T. M. Dunster
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions involve expon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::939a6ac89fff3a6615b52c4eb8928797
Publikováno v:
Constr Approx (2017) 46:645?675
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a25a27bf22c6a227d7bf7eece7e1e3ae
https://doi.org/10.1007/s00365-017-9372-8
https://doi.org/10.1007/s00365-017-9372-8
Autor:
T. M. Dunster
Publikováno v:
Journal of Classical Analysis. :1-21
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve elementar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4cdd75d6894717dc01547061bab5cb87
https://doi.org/10.7153/jca-11-01
https://doi.org/10.7153/jca-11-01