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

Abstract

In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.

On Fourier–Bessel matrix transforms and applications

“…Recently, many works on the Bessel function theory have been achieved, for example, by Agarwal et al, 20 Cortés et al, 21 Mondal and Akel, 22 Albayrak et al, 23 and Mubeen et al 24 Nowadays, special matrix functions have variety of uses in the field of probability theory, fractional operators, modeling of groundwater pumping, quantum algebraic techniques, and engineering sciences. Very recently, many authors work on these functions (for details, see the works of Abdalla, [25][26][27] Bakhet et al, 28 Dwivedi and Sahai, 29,30 Ismail et al, 31 He et al, 32,33 Khammash et al, 34 Srivastava et al, 35 and Zayed et al 36,37 ). One particular special matrix function that frequently appears in the recent studies and applications is the Bessel matrix function, which has been introduced and discussed in previous studies.…”

New extension of beta, Gauss and confluent hypergeometric functions

“…In 1730, Euler also introduced beta function, ( 1 , 2 ) for a pair of complex numbers 1 and 2 with real positive parts through the integrand. Later on, various extensions of classical gamma and beta functions were studied by renowned Mathematicians and proved to be significantly important in different areas of Applied Mathematics, Statistics, Physics and Engineering such as heat conduction, probability theory, Fourier, Laplace, K-transforms and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Definition 1.…”

On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

“…Applications of special matrix functions also grow and have become active areas in recent literature including statistics, Lie groups theory, and differential equations (see, e.g., [8][9][10][11] and elsewhere). New extensions of some of the well-known special matrix functions such as gamma matrix function, beta matrix function, and Gauss hypergeometric matrix function have been extensively studied in recent papers [12][13][14][15][16][17][18][19]. Our main purpose in this paper is to obtain an extension of the incomplete Gamma and Beta matrix functions and will be introduced as application to incomplete Bessel functions with matrix coefficients.…”