Hypergeometric Functions of 2 × 2 Matrix Argument are Expressible in Terms of Appell's Functions F 4

1978 ◽  
Vol 70 (1) ◽  
pp. 39
Author(s):  
Tom Koornwinder ◽  
Ida Sprinkhuizen-Kuyper
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Argument

scholarly journals Extended k-Gamma and k-Beta Functions of Matrix Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1715
Author(s):  
Ghazi S. Khammash ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Gamma Function ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Formula ◽  
Beta Function ◽  
Integral Representations ◽  
Matrix Argument ◽  
Functional Relations

Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

scholarly journals Laplace approximations for hypergeometric functions with matrix argument

2002 ◽  
Vol 30 (4) ◽  
pp. 1155-1177 ◽  
Author(s):  
Roland W. Butler ◽  
Andrew T. A. Wood
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Argument

IV.—On the Integrals of Hua and James.

1968 ◽  
Vol 68 (1) ◽  
pp. 54-69
Author(s):  
Henry Jack
Keyword(s):  
General Theory ◽  
Power Series ◽  
Lie Groups ◽  
Hypergeometric Functions ◽  
Spherical Function ◽  
Series Representation ◽  
Explicit Representation ◽  
Zonal Polynomials ◽  
Simple Lie Groups ◽  
Matrix Argument

SynopsisRecently a power series representation of Hypergeometric functions with matrix argument has been established. This representation involves a special type of spherical function from the theory of semi-simple Lie groups, called the zonal polynomials. A general theory of these polynomials is well established; however an explicit representation of them is lacking. This paper considers two integrals which are related to this explicit representation. The final paragraph considers a third integral which gives an application of a result from a previous paper of the author.

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