RETRACTED: On Humbert matrix functions

On Certain Arithmetical Functions Due to G. Humbert

1. Introduction. G. Humbert has discussed, in a series of brief notes, 1 a certain class of entire functions with interesting arithmetical properties. These functions are defined, in an essentially unique manner , by certain functional equations. The Fourier series representations of the solutions of these equations are similar in form to those for the elliptic functions snu y cnu, dnu, and so ...

A New Extension of Humbert Matrix Function and Their Properties

Special matrix functions appear in the literature related to statistics [1-4] and more recently in connection with matrix analogues of Laguerre, Hermite and Legendre differential equations and the corresponding polynomial families [5-7]. The connection between the Humbert matrix function and modified Bessel matrix function has been established in [8,9]. In recent papers [10,11], we defined and ...

The Matrix Version for the Multivariable Humbert Polynomials

In this paper, the matrix extension of the multivariable Humbert polynomials is introduced. Various families of linear, multilinear and multilateral generating matrix functions of these matrix polynomials are presented. Miscellaneous applications are also discussed. 2000 Mathematics Subject Classification: 33C25; 15A60

On Humbert matrix function of two complex variables under differential operator

Lommel Matrix Functions

The main objective of this work is to develop a pair of Lommel matrix functions suggested by the hypergeometric matrix functions and some of their properties are studied. Some properties of the hypergeometric and Bessel matrix functions are obtained.