Extended k-Gamma and k-Beta Functions of Matrix Arguments
Ghazi S. Khammash, Praveen Agarwal, Junesang Choi
Abstract
Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.
Topics & Concepts
Beta function (physics)Matrix functionGamma functionBETA (programming language)MathematicsMatrix (chemical analysis)Function (biology)Hypergeometric functionPure mathematicsPascal matrixHypergeometric function of a matrix argumentGeneralized hypergeometric functionSymmetric matrixPhysicsQuantum mechanicsComputer scienceEvolutionary biologyComposite materialQuantum gravityMaterials scienceQuantumEigenvalues and eigenvectorsBiologyProgramming languageRelationship between string theory and quantum field theoryAdvanced Statistical Methods and ModelsMathematical Inequalities and ApplicationsMulti-Criteria Decision Making