Asymptotics of the Gauss hypergeometric function with large parameters, I

DOI10.7153/jca-02-15zbMath1412.33008OpenAlexW2564401611MaRDI QIDQ3120697

Richard B. Paris

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jca-02-15

zbMATH Keywords

asymptotic expansionhypergeometric functionslarge parameters

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Classical hypergeometric functions, ({}_2F_1) (33C05) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (13)

Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps ⋮ Connection coefficients for ultraspherical polynomials with argument doubling and generalized bispectrality ⋮ On the density arising from the domain of attraction of an operator interpolating between sum and supremum: the \(\alpha\)-sun operator ⋮ The difference between two random mixed quantum states: exact and asymptotic spectral analysis ⋮ Testing in high-dimensional spiked models ⋮ Central limit theorems for the real eigenvalues of large Gaussian random matrices ⋮ 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 ⋮ Spectral density functions of bivariable stable polynomials ⋮ Area propagator and boosted spin networks in loop quantum gravity ⋮ The hypergeometric function, the confluent hypergeometric function and WKB solutions ⋮ ASYMPTOTICS OF A GAUSS HYPERGEOMETRIC FUNCTION WITH TWO LARGE PARAMETERS: A NEW CASE ⋮ Asymptotics of the Gauss hypergeometric function with large parameters, II

Uses Software

• DLMF

Cites Work

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• The special functions and their approximations. Vol. I, II
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• Asymptotics of the Gauss hypergeometric function with large parameters, II
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• 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
• Diffraction by, or diffusion into, a penetrable wedge
• The hodograph transformation in trans-sonic flow. II. Auxiliary theorems on the hypergeometric functions ψ _n (ז)
• Asymptotic expansions for the hypergeometric functions occurring in gas-flow theory

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