• On the inverse Laplace transform of the product of a general class of polynomials and the multivariable H-function

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/100/01/0021-0024

• Keywords

The Laplace transform; the multivariable H-function; a general class of polynomials

• Abstract

In this paper we evaluate the inverse Laplace transform of$$\begin{gathered} s^{ - \eta } (s^{l_1 } + \lambda _1 )^{ - \sigma } (s^{l_2 } + \lambda _2 )^{ - \rho } \hfill \\ \times S_n^m [xs^{ - W} (S^{l_1 } + \lambda _1 )^{ - \upsilon } (S^{l_2 } + \lambda _2 )^{ - w} ]S_{n'}^{m'} [ys^{ - w'} (S^{l_1 } + \lambda _1 )^{ - \upsilon '} (S^{l_2 } + \lambda _2 )^{ - w_r } ] \hfill \\ \times H[z_1 s^{ - W_1 } (S^{l_1 } + \lambda _1 )^{ - \upsilon _1 } (S^{l_2 } + \lambda _2 )^{ - w_1 } ,...,z_r s^{ - w_r } (S^{l_1 } + \lambda _1 )^{ - \upsilon _r } (S^{l_2 } + \lambda _2 )^{ - w'} ] \hfill \\ \end{gathered}$$

Due to the general nature of the multivariable H-function involved herein, the inverse Laplace transform of the product of a large number of special functions involving one or more variables, occurring frequently in the problems of theoretical physics and engineering sciences can be obtained as simple special cases of our main findings. For the sake of illustration, we obtain here the inverse Laplace transform of a product of the Hermite polynomials, the Jacobi polynomials andr different modified Bessel functions of the second kind. A theorem obtained by Srivastava and Singh[7] follows as a special case of our main result.

• Author Affiliations

1. Department of Mathematics, M. R. Engineering College, Jaipur - 302 017, India

• Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019