Search

Motivated by recent investigations, the main object of this paper is to construct the new (p, q)-analogy definitions of the various families of (p, q)-Bessel functions using the generating function method as a starting point. We derive the explicit representations, especially differential recurrence relations and these classes results of the (p, q)-Bessel functions. [ABSTRACT FROM AUTHOR]

The main aim of this present paper is to investigate a new of interesting generating matrix relation for Legendre matrix polynomials with the help of a Lie group-theoretic method. Certain properties are well known but some of them are believed to be novel families of matrix differential recurrence relations and generating matrix functions for these matrix polynomials. Special cases of new results are also given here as applications. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to construct new p , q -analogy definitions of various families of p , q -Humbert functions using the generating function method as a starting point. This study shows a class of several results of p , q -Humbert functions with the help of the generating functions such as explicit representations and recurrence relations, especially differential recurrence relations, and prove some of their significant properties of these functions. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to construct new analogous definitions of the families of Humbert functions using the generating function method as the starting point. We study a class of various results in the family of Humbert functions with the help of the families of generating functions, explicit representations, especially differential recurrence relations and study some of the significant properties of this family of functions. [ABSTRACT FROM AUTHOR]

In this study, some new and known finite sums, operational formulas and generating matrix relations for Konhauser matrix polynomials of the second kind are given. [ABSTRACT FROM AUTHOR]

The main aim of this work is to give a different approach to the proof of some properties for Ultraspherical matrix polynomials (UMPs). We obtain the connections between Laguerre, Hermite and Ultraspherical matrix polynomials. Some definitions of new families of Ultraspherical matrix polynomials are given. Finally, various families of linear, bilinear and bilateral generating matrix functions (GMFs) for UMPs are given. [ABSTRACT FROM AUTHOR]

The aim of this present paper is to investigate an interesting generating matrix relations for generalized Hermite-type matrix polynomials by the application of the Lie group-theoretic method. Based on the Weisner's group theoretic method, we derived some properties for these generalized Hermite-type matrix polynomials. Some applications of the result are also given here. [ABSTRACT FROM AUTHOR]