On the matrix version of extended Bessel functions and its application to matrix differential equations
Ahmed Bakhet, Fuli He, Mimi Yu
Abstract
In this paper, we focus on the extensions of the Bessel matrix function and the modified Bessel matrix function. We first introduce the extended Bessel matrix function and the extended modified Bessel matrix function of the first kind by using the extended Beta matrix function. Then we establish the integral representations, differentiation formula, and hypergeometric representation of such functions. Finally, as an application, we study a kind of second-order matrix differential equations. We prove that the extended modified Bessel matrix function is a particular solution to this kind of differential equations.
Topics & Concepts
Bessel functionMatrix functionStruve functionMathematicsBessel polynomialsMatrix (chemical analysis)Pascal matrixSingle-entry matrixMathematical analysisSymmetric matrixSquare matrixBessel processDifferential equationMatrix representationPure mathematicsPhysicsJacobi polynomialsGroup (periodic table)Classical orthogonal polynomialsGegenbauer polynomialsComposite materialMaterials scienceQuantum mechanicsEigenvalues and eigenvectorsOrthogonal polynomialsMacdonald polynomialsMathematical functions and polynomialsMatrix Theory and AlgorithmsNonlinear Waves and Solitons