Certain q-Integrals Involving the Generalized Hypergeometric and Basic Hypergeometric Functions

2018 ◽  
Vol 6 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Javid Ahmad Ganie ◽  
Altaf Ahmad ◽  
Renu Jain
Keyword(s):  
Hypergeometric Functions ◽  
Basic Hypergeometric Functions

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.

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.

A Transformation Connecting Products of Generalised Basic Hypergeometric Functions

1968 ◽  
Vol 11 (2) ◽  
pp. 241-248
Author(s):  
Arun Verma
Keyword(s):  
Hypergeometric Functions ◽  
Basic Hypergeometric Functions

Darling [2] in 1932 gave two types (equations 11 and 18) of transformations connecting generalised hyper geometric functions. The first was studied by Bailey [1] and extended by Sears [4] to a transformation connecting products of basic hyper geometric functions of the type r+1ϕr × r+1ϕr. In a number of papers [6, 7, 8] the author has extended these results to both unilateral and bilateral series with bases q and q1/2. The second type of transformation by Darling for a product 0F1 × 3F2 was extended by Bailey [1] to a transformation between 1F0 × r+1Fr. In the same paper Bailey mentioned the transformation of a 0ϕ1 × 3ϕ2 without proof.

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