Uniform asymptotic expansions for hypergeometric functions with large parameters IV

DOI10.1142/S0219530514500389zbMath1300.33007OpenAlexW4246122464MaRDI QIDQ2931004

Sarah Farid Khwaja, A. B. Olde Daalhuis

Publication date: 21 November 2014

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530514500389

zbMATH Keywords

uniform asymptotic approximationsGauss hypergeometric functionBleistein method

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Asymptotic representations in the complex plane (30E15)

Related Items (14)

The double pentaladder integral to all orders ⋮ Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps ⋮ Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank $1$ ⋮ Contiguous relations, Laplace's methods, and continued fractions for \({}_3F_2(1)\) ⋮ An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle ⋮ Asymptotic analysis via calculus of hypergeometric functions ⋮ The mean value of symmetric square \(L\)-functions ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ Non-vanishing of Maass form symmetric square \(L\)-functions ⋮ New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials ⋮ Large-Parameter Asymptotic Expansions for the Legendre and Allied Functions ⋮ Asymptotics of the generalized Gegenbauer functions of fractional degree ⋮ The hypergeometric function, the confluent hypergeometric function and WKB solutions ⋮ The second moment of symmetric square L-functions over Gaussian integers

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Computing toroidal functions for wide ranges of the parameters
• Asymptotics of the hypergeometric function
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• Uniform Airy-Type Expansions of Integrals
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS II
• Rawlin's method and the diaphonous cone
• Exponentially accurate uniform asymptotic approximations for integrals and Bleistein's method revisited
• Uniform asymptotic expansions of integrals with stationary point near algebraic singularity

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