Integrals with nearly coincident branch points: Gegenbauer polynomials of large degree

DOI10.1098/rspa.2006.1787zbMath1257.33017OpenAlexW1988870791MaRDI QIDQ5438812

F. Ursell

Publication date: 8 February 2008

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2006.1787

zbMATH Keywords

uniform asymptoticsloop integralsmaximum-modulus principle

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of hypergeometric functions (33C90) Representations of entire functions of one complex variable by series and integrals (30D10)

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Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method ⋮ Uniform asymptotic methods for integrals

Cites Work

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