On the Certain Properties and Results of Incomplete Generalized Hypergeometric Functions with Matrix Argument

Abstract

This study aims to assess the generalized matrix transform (M-transform) of various incomplete types of special functions named generalized incomplete hypergeometric functions, incomplete H-functions, incomplete H functions, incomplete I-functions, all of which possess a matrix argument. The matrix argument in this case is a real symmetric positive definite matrix of size k × k having k(k+1) 2
variables. Here, we establish the special functions with a matrix argument by extending the existing special functions with a scalar argument. Both scalar and matrix arguments are significant in statistical distribution problems, particularly in scenarios where the null hypothesis is not assumed to be true. Additionally, we derived specific cases by extending the univariate cases.