A study on Horn matrix functions and its confluent cases

2022/11/15 by Dr Ravi Dwivedi, Dwivedi, Ravi
Engineering · Mathematics · #Advanced Mathematical Identities #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2211.08172

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. We also give the certain integral representation of these hypergeometric matrix functions. The study of these 23 matrix functions leads to completing the matrix generalization of Horn's list of 34 hypergeometric series.

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