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About 4,008 papers for “Hypergeometric function”

The Hypergeometric Function

E. T. Whittaker, G. N. Watson · Cambridge University Press eBooks · 1996

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Cited by 1

Gauss Hypergeometric Function

Ravi Dwivedi · 2024

This book presents a novel journey of the Gauss hypergeometric function and contains the different versions of the Gaussian hypergeometric function, including its classical version. In particular, the $q$-Gauss or basic Gauss hypergeometric function, Gauss hypergeometric function with matrix arguments, Gauss hypergeometric function with matrix parameters, the matrix-valued Gauss hypergeometric function, the finite field version, the extended Gauss hypergeometric function, the $(p, q)$- Gauss hypergeometric function, the incomplete Gauss hypergeometric function and the discrete analogue of Gauss hypergeometric function. All these forms of the Gauss hypergeometric function and their properties are presented in such a way that the reader can understand the working algorithm and apply the same for other special functions. This book is useful for UG and PG students, researchers and faculty members working in the field of special functions and related areas.

Cited by 7

The hypergeometric function, the confluent hypergeometric function and WKB solutions

Takashi Aoki, Toshinori Takahashi, Mika Tanda · Journal of the Mathematical Society of Japan · 2021

Relations between the hypergeometric function with a large parameter and Borel sums of WKB solutions of the hypergeometric differential equation with the large parameter are established. The confluent hypergeometric function is also investigated from the viewpoint of exact WKB analysis. As applications, asymptotic expansion formulas for those classical special functions with respect to parameters are obtained.

Cited by 6

THE CONFLUENT HYPERGEOMETRIC FUNCTION

A. Erdélyi · Bulletin of the London Mathematical Society · 1970

By Herbert Buchholz: pp. xvi, 238; DM 64. US$16 (Springer-Verlag, Berlin 1969).

Cited by 71

The Confluent Hypergeometric Function

Harold Jeffreys, Bertha Jeffreys · Cambridge University Press eBooks · 1999

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

Cited by 8

A Hypergeometric Function Integral

S. Lj. Damjanovia · SIAM Review · 1985

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistoryPublished online: 17 February 2012Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for Industrial and Applied MathematicsCODEN: siread

Cited by 0

Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

Komal Singh Yadav, Bhagwat Sharan, Ashish Verma · Analysis · 2024

Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.

Cited by 0

hypergeo: The Gauss Hypergeometric Function

Robin K. S. Hankin · 2008

The Gauss Hypergeometric Function Version 1.2-14 Depends R (>= 3.1.0),Imports elliptic (>= 1.3-5), contfrac (>= 1.1-9), deSolve

Cited by 11Open access