A note on hypergeometric functions of matrix arguments
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Present study explores the extension of hypergeometric functions using matrix arguments, focusing on the Gauss and Wright-type generalized hypergeometric functions viz. ${}_2F_1, {}_2R_1, {}_pR_q, {}_p{\psi}_q$. Using fou-ndational concepts like Pochhammer symbol and gamma function of matrix arguments, analogues of above functions have been introduced in matrix arguments using zonal polynomials, and several properties of which have been studied, contributing to the development in the theory of special functions, opening pathways for new research.
Abstract
Present study explores the extension of hypergeometric functions using matrix arguments, focusing on the Gauss and Wright-type generalized hypergeometric functions viz. ${}_2F_1, {}_2R_1, {}_pR_q, {}_p{\psi}_q$. Using fou-ndational concepts like Pochhammer symbol and gamma function of matrix arguments, analogues of above functions have been introduced in matrix arguments using zonal polynomials, and several properties of which have been studied, contributing to the development in the theory of special functions, opening pathways for new research.