scholarly journals Generating functions on extended Jacobi polynomials from Lie group view point

1996 ◽  
Vol 40 ◽  
pp. 3-13 ◽  
Author(s):  
M. C. Mukherjee
Keyword(s):  
Lie Group ◽  
Generating Functions ◽  
Jacobi Polynomials ◽  
View Point

scholarly journals Some generating functions of modified Bessel polynomials from the view point of Lie group

1984 ◽  
Vol 7 (4) ◽  
pp. 823-825 ◽  
Author(s):  
Asit Kumar Chongdar
Keyword(s):  
Lie Group ◽  
Generating Functions ◽  
View Point ◽  
Bessel Polynomials

In this paper we have derived a class of bilateral generating relation for modified Bessel polynomials from the view point of Lie group. An application of our theorem is also pointed out.

scholarly journals Operational Methods in the Study of Sobolev-Jacobi Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 124 ◽  
Author(s):  
Nicolas Behr ◽  
Giuseppe Dattoli ◽  
Gérard Duchamp ◽  
Silvia Penson
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Hermite Polynomials ◽  
Umbral Calculus ◽  
Generalized Hypergeometric Functions ◽  
Normal Ordering ◽  
Gamma Functions ◽  
Image Technique ◽  
Operational Methods

Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called umbral image technique. Besides providing a class of new formulae for generalized hypergeometric functions and an implementation of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of Sobolev-Jacobi polynomials. Motivated by applications to theoretical chemistry, we moreover present a deep link between generalized normal-ordering techniques introduced by Gurappa and Panigrahi, two-variable Hermite polynomials and our integral-based series transforms. Notably, we thus calculate all K-tuple L-shifted lacunary exponential generating functions for a certain family of Sobolev-Jacobi (SJ) polynomials explicitly.

scholarly journals On the p,q-Humbert Functions from the View Point of the Generating Function Method

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ayman Shehata
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Function Method ◽  
Recurrence Relations ◽  
View Point ◽  
Starting Point ◽  
Explicit Representations

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.

Bilateral generating functions involving Jacobi polynomials

1969 ◽  
Vol 66 (1) ◽  
pp. 105-107 ◽  
Author(s):  
H. L. Manocha
Keyword(s):  
Generating Functions ◽  
Jacobi Polynomial ◽  
Jacobi Polynomials ◽  
Image Position ◽  
Bilateral Generating Functions

In paper(1) it has been proved thatwhere the Jacobi polynomial is denned as ((3), p. 255)

scholarly journals Some generating functions for the Jacobi polynomials

1992 ◽  
Vol 23 (10) ◽  
pp. 51-56 ◽  
Author(s):  
H.M. Srivastava ◽  
R.K. Saxena ◽  
Z. Hussain
Keyword(s):  
Generating Functions ◽  
Jacobi Polynomials

scholarly journals Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions

2018 ◽  
Vol 3 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Ahmed Ali Atash ◽  
Hussein Saleh Bellehaj
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
General Transformation ◽  
Summation Theorem ◽  
Transformation Formulas

AbstractIn this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions K5 and K12 by application of the generalized Kummer’s summation theorem. Further, a number of generating functions for Jacobi polynomials are also derived as an applications of our main results.

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