The Gauss hypergeometric function \(F(a,b;c;z)\) for large \(c\)

DOI10.1016/j.cam.2005.11.027zbMath1106.33004OpenAlexW1995850365MaRDI QIDQ2433775

Ester Pérez Sinusía, Chelo Ferreira, José Luis López

Publication date: 30 October 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.11.027

zbMATH Keywords

asymptotic expansionsGauss hypergeometric function

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (7)

Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps ⋮ Monotonicity properties of generalized elliptic integrals with respect to the parameter ⋮ Rényi entropies, \(L_q\) norms and linearization of powers of hypergeometric orthogonal polynomials by means of multivariate special functions ⋮ Acceleration of generalized hypergeometric functions through precise remainder asymptotics ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ On certain results related to the hypergeometric function \(F_K\) ⋮ A simplification of Laplace's method: applications to the gamma function and Gauss hypergeometric function

Cites Work

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• Hypergeometric functions
• Asymptotische Entwicklungen der Gaußschen hypergeometrischen Funktion für unbeschränkte Parameter. (Asymptotic expansions of the Gauss hypergeometric function for unbounded parameters)
• Asymptotische Darstellungen der hypergeometrischen Funktionen für große Werte eines Parameters
• Large parameter cases of the Gauss hypergeometric function
• Incomplete gamma functions for large values of their variables
• Asymptotics of the hypergeometric function
• ASYMPTOTISCHE ENTWICKLUNGEN DER HYPERGEOMETRISCHEN FUNKTION F(a, b, c, z) FÜR IcI →∞ UND KONSTANTE WERTE a, b UND z
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS II

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