A Note on the Appell Hypergeometric Matrix Function F₂

Abstract

In this article, we introduce some of the mathematical properties of the second Appell hypergeometric matrix function F2(A, B1, B2, C1, C2; z, w) including integral representations, transformation formulas, and series formulas.

Certain fractional formulas of the extended k-hypergeometric functions

“…In 1813, Gauss first summarized his investigations of hypergeometric functions, which has been of great significance in the mathematical modeling of physical phenomena and other applications. Recently, various developments and expansions of the hypergeometric functions have been proposed and discussed (for example, see [1][2][3][4][5][6][7][8][9][10][11][12]).…”

Further Results on the p , k − Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators

“…Recently, various extensions of the hypergeometric functions have been presented and investigated (see, for example, [1][2][3][4][5][6][7]).…”

On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

“…We say that if Re(ξ) for all ξ ∈ σ(A), a matrix A in C r×r is a positive stable matrix. In [9,[17][18][19], if f(z) and g(z) are holomorphic functions in an open set Λ of the complex plane and if A is a matrix in C r×r for which σ(A) ⊂ Λ, then f(A)g(A) � g(A)f(A).…”