A study of generalized hypergeometric Matrix functions <i>via</i> two-parameter Mittag–Leffler matrix function
Shilpi Jain, Rahul Goyal, Georgia Irina Oros, Praveen Agarwal, Shaher Momani
Abstract
Abstract The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function. In particular, we investigate certain important properties of these extended matrix functions such as integral representations, differentiation formulas, beta matrix transform, and Laplace transform. Furthermore, we introduce an extension of the Jacobi matrix orthogonal polynomial by using our generalized Gauss hypergeometric matrix function, which is very important in scattering theory and inverse scattering theory.
Topics & Concepts
Hypergeometric function of a matrix argumentMatrix functionGeneralized hypergeometric functionMathematicsBasic hypergeometric seriesPascal matrixMatrix (chemical analysis)Confluent hypergeometric functionHypergeometric identityPure mathematicsInvolutory matrixSingle-entry matrixHypergeometric functionMathematical analysisAlgebra over a fieldSymmetric matrixPhysicsMaterials scienceEigenvalues and eigenvectorsComposite materialQuantum mechanicsMathematical functions and polynomialsMatrix Theory and AlgorithmsQuantum Mechanics and Non-Hermitian Physics