scholarly journals Bilinear generating relations for a family of q-polynomials and generalized basic hypergeometric functions

2012 ◽  
Vol 16 (2) ◽  
pp. 191-199
Author(s):  
S. D. Purohit ◽  
V. K. Vyas ◽  
R. K. Yadav
Keyword(s):  
Generating Function ◽  
General Class ◽  
Hypergeometric Functions ◽  
Hypergeometric Polynomials ◽  
Basic Hypergeometric Functions ◽  
Generating Relations ◽  
Basic Analogue ◽  
Fox’S H Function

In this paper, we derive a bilinear q-generating function involving basic analogue of Fox's H-function and a general class of q-hypergeometric polynomials. Applications of the main results are also illustrated.

scholarly journals A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1161
Author(s):  
Hari Mohan Srivastava ◽  
Sama Arjika
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Additional Parameter ◽  
Physical Sciences ◽  
General Family ◽  
Hypergeometric Polynomials

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.

scholarly journals Some Srivastava-Brafman Type Generating Relations For A General Class Of Multi-Index And Multi-Variable Gould-Hopper And Dattoli Type Hypergeometric Polynomials

2014 ◽  
Vol 10 (1) ◽  
pp. 31-44
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Ram Pal
Keyword(s):  
Hypergeometric Function ◽  
General Class ◽  
Multiple Series ◽  
Multi Index ◽  
Hypergeometric Polynomials ◽  
New Family ◽  
Different Types ◽  
Generating Relations ◽  
Multiple Sequences

Abstract In this article, we first introduce and study a new family of the multi-index and multi-variable Gould-Hopper and Dattoli type polynomials {Hn(cm, cm-1,…, c3, c2)(a1, a2, …, am} defined by (2.1), which are an extension of different types of Her-mite polynomials defined in section 1. We next consider multi-variable linear, bilinear and bilateral generating relations of the newly defined hypergeometric polynomials, using series iteration techniques. Further, we generalize these generating relations in the forms of multiple series identities involving bounded multiple sequences, Fox-Wright hypergeometric function and Srivastava-Daoust multi-variable hypergeometric function.

scholarly journals An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2238
Author(s):  
Rahul Goyal ◽  
Praveen Agarwal ◽  
Alexandra Parmentier ◽  
Clemente Cesarano
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Derivative Operator ◽  
The Family ◽  
Generating Relations ◽  
Fractional Derivative Operators ◽  
Extended Operator ◽  
Two Parameter

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.

QUANTUM DEFORMATIONS OF QUANTUM MECHANICS

1993 ◽  
Vol 08 (01) ◽  
pp. 89-96 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Evolution ◽  
Function Space ◽  
Scalar Product ◽  
Hypergeometric Functions ◽  
Quantum Mechanical ◽  
Basic Hypergeometric Functions ◽  
Quantum Deformations ◽  
The One

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

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