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 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 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 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 Finite Integral Formulas Involving Multivariable Aleph-Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Hagos Tadesse ◽  
D. L. Suthar ◽  
Minilik Ayalew
Keyword(s):  
Mathematical Analysis ◽  
General Class ◽  
Jacobi Polynomials ◽  
Special Functions ◽  
Mathematical Physics ◽  
Legendre Functions ◽  
Algebraic Functions ◽  
Integral Formulas ◽  
General Class Of Polynomials ◽  
Finite Integral

The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics.

scholarly journals Certain Fractional Derivative Formulae Involving the Product of a General Class of Polynomials and the Multivariable Gimel-Function

2018 ◽  
pp. 1-13
Author(s):  
Frédéric Ayant
Keyword(s):  
Fractional Derivative ◽  
General Class ◽  
Leibniz Rule ◽  
General Character ◽  
General Class Of Polynomials

In the present paper, we obtain three unified fractional derivative formulae. The first involves the product of a general class of polynomials and the multivariable Gimel-function. The second involves the product of a general class of polynomials and two multivariable Gimel-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives.The last fractional derivative formulae also involves the product of a general class of polynomials and the multivariable Gimel-function but it is obtained by the application of the first fractional derivative formulae twice and, it involve two independents variables instead of one.The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the type The formulae are the very general character and thus making them useful in applications. In the end, we shall give a particular case.

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