Open AccessOn A Matrix Hypergeometric Differential Equation
Author(s) -
Salah S. Hamd,
Faisal Saleh Abdalla,
Ahmed Shletiet
Publication year - 2021
Publication title -
mağallaẗ al-ʿulūm al-baḥṯaẗ wa-al-taṭbīqiyyaẗ
Language(s) - English
Resource type - Journals
eISSN - 2708-8251
pISSN - 2521-9200
DOI - 10.51984/jopas.v20i1.1303
Subject(s) - frobenius solution to the hypergeometric equation , confluent hypergeometric function , hypergeometric function of a matrix argument , basic hypergeometric series , generalized hypergeometric function , riemann's differential equation , matrix function , mathematics , hypergeometric function , hypergeometric identity , matrix differential equation , homogeneous differential equation , matrix (chemical analysis) , bilateral hypergeometric series , differential equation , mathematical analysis , pure mathematics , ordinary differential equation , symmetric matrix , physics , differential algebraic equation , riemann zeta function , eigenvalues and eigenvectors , materials science , quantum mechanics , riemann xi function , composite material
In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation. The aim of this work is to extend a well known theorem on Hypergeometric function in the complex plane to a matrix version, and we show that the asymptotic expansions of Hypergeometric function in the complex plane ” that are given in the literature are special members of our main result. Background and motivation are discussed.