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Generalized hypergeometric function

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Is there a way to convert functions to hypergeometric functions ...

(PDF) On q-hypergeometric functions

(PDF) Hypergeometric Functions - DOKUMEN.TIPS

(PDF) Certain Properties of the Generalized Gauss Hypergeometric ...

Generalized hypergeometric functions | Real and complex analysis ...

Hyperbola and the hypergeometric functions (í µí°¾ = 1). | Download ...

(PDF) Geometric Properties of Generalized Hypergeometric Functions

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hypergeometric functions

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terminology - Why are the hypergeometric functions called ...
Bessel functions in terms of the confluent hypergeometric function
Relation between hypergeometric and gamma functions
Does $\\sin(x)$ and $\\cos(x)$ have representations as …
calculus - Product of two hypergeometric functions - Mathematics …
Product of two generalized hypergeometric functions
What is the reason to use hypergeometric functions?
Hypergeometric functions & integral - Mathematics Stack Exchange
reference request - Tables of Hypergeometric Functions
Asymptotics of Hypergeometric - Mathematics Stack Exchange

terminology - Why are the hypergeometric functions called ...

Apr 12, 2018 · I was wondering where the term "hypergeometric" for the hypergeometric function $_2F_1(a, b; c; z)$ comes from. Wikipedia says that the term was coined by J. Wallis, but I couldn't find any (mathematical) reason why these functions are anything like hyper-geometric.

Bessel functions in terms of the confluent hypergeometric function

Jul 22, 2020 · From here, I don't know how one could go further, for example, how to get rid of the exponential term and etc., and to reproduce the representation of the Bessel functions as given in the beginning of this post.

Relation between hypergeometric and gamma functions

Oct 30, 2015 · Relation between hypergeometric and gamma functions. Ask Question ... Special value of hypergeometric ...

Does $\\sin(x)$ and $\\cos(x)$ have representations as …

Feb 7, 2021 · If you really want to look up details the NIST Handbook of Mathematical Functions is a great (but large and fairly expensive) reference book. Chapter 15, p386 gives plenty of examples of elementary functions that can be written as special cases of the hypergeometric function.

calculus - Product of two hypergeometric functions - Mathematics …

Nov 23, 2015 · This product of two Gaussian hypergeometric functions can be expressed by a sum over generalized hypergeometric functions ${}_{4}F_{3}$ according to formula 4.3.(14) on page 187 in "Higher Transcendental Functions, Vol. 1" by A. Erdelyi (Ed.).

Product of two generalized hypergeometric functions

Nov 7, 2016 · Yes, there is a general result, via which this can be cast in terms of the $_2F_1$ hypergeometric function. The relevant relation is formula 4.3.(12) on page 187 in " Higher Transcendental Functions, Vol. 1 " by A. Erdelyi (Ed.), which I …

What is the reason to use hypergeometric functions?

$\begingroup$ Let's take your second sum as an example; it turns out that knowing the $-m$ numerator parameter is a negative integer is crucial, since it is a known property of hypergeometric functions that they degenerate to polynomials whenever one or both of their numerator parameters are negative. $\endgroup$ –