On Some Applications Related To Fox's H-Functions Of Two Variables
MSC 2010: 44A15, 44A20, 33C60Using the generalized confluent hypergeometric function [6] some new integral transforms are introduced. They are generalizations of some classical integral transforms, such as the Laplace, Stieltjes, Widder-potential, Glasser etc. integral transforms. The basic properties of these generalized integral transforms and their inversion formulas are obtained. Some examples are also given.
Certain generalizations of Sister Celine’s polynomials are given which include most of the known polynomials as their special cases. Besides, generating functions and integral representations of these generalized polynomials are derived and a relation between generalized Laguerre polynomials and generalized Bateman’s polynomials is established.
The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.
MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05The 6th International Conference "Transform Methods and Special Functions' 2011", 20 - 23 October 2011 was dedicated to the 80th anniversary of Professor Peter Rusev, as one of the founders of this series of international meetings in Bulgaria, since 1994. It is a pleasure to congratulate the Jubiliar on behalf of the Local Organizing Committee and International Steering Committee, and to present shortly some of his life achievements...
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.