scholarly journals Certain Finite Integrals Related to the Products of Special Functions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2013
Author(s):  
Dinesh Kumar ◽  
Frédéric Ayant ◽  
Suphawat Asawasamrit ◽  
Jessada Tariboon
Keyword(s):  
General Class ◽  
Special Functions ◽  
Several Variables ◽  
General Class Of Polynomials ◽  
Engineering Sciences ◽  
Special Cases ◽  
Finite Integrals

The aim of this paper is to establish a theorem associated with the product of the Aleph-function, the multivariable Aleph-function, and the general class of polynomials. The results of this theorem are unified in nature and provide a very large number of analogous results (new or known) involving simpler special functions and polynomials (of one or several variables) as special cases. The derived results lead to significant applications in physics and engineering sciences.

scholarly journals A unified inverse Laplace transform formula involving the product of a general class of polynomials and the Fox $H$-function

2005 ◽  
Vol 36 (2) ◽  
pp. 87-92
Author(s):  
R. C. Soni ◽  
Deepika Singh
Keyword(s):  
Laplace Transform ◽  
General Class ◽  
Special Functions ◽  
Inverse Laplace Transform ◽  
General Class Of Polynomials ◽  
Special Cases ◽  
Main Formula

In the present paper we obtain the inverse Laplace transform of the product of a general class of polynomials and the Fox $H$-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. Therefore, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions can be obtained as simple special cases of our main result. The results obtained by Gupta and Soni [2] and Srivastava [5] follow as special cases of our main result.

scholarly journals An Integral Involving Certain General Class of Polynomials and the Special Functions

2014 ◽  
Vol 10 (1) ◽  
pp. 07-13
Author(s):  
Ashok Singh Shekhawat ◽  
◽  
Parul Gupta ◽  
Rakeshwar Purohit
Keyword(s):  
General Class ◽  
Special Functions ◽  
General Class Of Polynomials

scholarly journals Fractional derivatives of certain special functions

2001 ◽  
Vol 32 (2) ◽  
pp. 103-109
Author(s):  
V. B. L. Chaurasia ◽  
Anju Godika
Keyword(s):  
General Class ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Leibniz Rule ◽  
Special Cases ◽  
Derivatives Of

The theorems relating to the fractional derivatives for the multivariable H-function [1,15,17] and a general class of multivariable polynomials [13] have been established in this paper. Use of well known generalized Leibniz rule has been made to derive some theorems. Certain special cases of the main theorems have also been discussed.

scholarly journals The two dimensional generalized Weyl fractional calculus and special functions

2010 ◽  
Vol 41 (2) ◽  
pp. 139-148
Author(s):  
V. B. L. Chaurasia ◽  
Mukesh Agnihotri
Keyword(s):  
Fractional Calculus ◽  
General Class ◽  
Special Functions ◽  
Fractional Integration ◽  
Two Dimensional ◽  
General Class Of Polynomials ◽  
Weyl Fractional Calculus

The object of this present paper is to derive a relation between the two dimensional I-transform involving a general class of polynomials and the Weyl type two dimensional Saigo operators of fractional integration. The results derived here are general in nature and include the results given earlier by Saigo, Saxena and Ram [10],Saxena and Ram [8], Saxena and Kiryakova [9] and Chaurasia and Srivastava [12].

scholarly journals Summation Formulas Obtained by Means of the Generalized Chain Rule for Fractional Derivatives

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
S. Gaboury ◽  
R. Tremblay
Keyword(s):  
General Formula ◽  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Mathematical Physics ◽  
Chain Rule ◽  
Generalized Hypergeometric Functions ◽  
Summation Formulas ◽  
Several Variables ◽  
Special Cases

In 1970, several interesting new summation formulas were obtained by using a generalized chain rule for fractional derivatives. The main object of this paper is to obtain a presumably new general formula. Many special cases involving special functions of mathematical physics such as the generalized hypergeometric functions, the Appell F1 function, and the Lauricella functions of several variables FD(n) are given.

scholarly journals Certain Feynman type integrals involving generalized k-Mittag-Leffler function and general class of polynomials

2019 ◽  
Vol 13 (3) ◽  
pp. 746-773
Author(s):  
Praveen Agarwal ◽  
Mehar Chand ◽  
Sugandh Rani ◽  
Themistocles Rassias
Keyword(s):  
General Class ◽  
Laguerre Polynomials ◽  
General Nature ◽  
General Class Of Polynomials ◽  
Special Cases

In the present paper, certain Feynman type integrals involving the generalized k-Mittag-Leffler function and the general class of polynomials are established and further extended these results involving Laguerre polynomials. On account of the most general nature of the functions involved therein, our main findings are capable of yielding a large number of new, interesting, and useful integrals, expansion formulas involving the generalized k-Mittag-Leffler function, and the Laguerre polynomials as their special cases.

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