On the inverse Laplace transform of special functionscontaining the Rodrigues type polynomial

Abstract

In the present paper, we obtain the inverse Laplace transform involving the product of a general class of polynomials \(\prod_{i=1}^{m} S_{n_i}^{\alpha_i, \beta_i}(x)\), the polynomial set \(S_{n}^{\alpha, \beta, 0}[x]\), and the H-function of several complex variables. On account of the most general character of the general class of polynomials, generalized polynomial set and the H-function of several complex variables involved, 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 particular cases of our main findings. For the sake of illustration, we obtain the inverse Laplace transform of product of two generalized Hermite polynomials given by Gould and Hopper [9], and the H-function of several complex variables. Our result provides a unification of the inverse Laplace transform pertaining to the product of polynomials and special functions earlier obtained by Soni and Singh [14,15], Gupta and Soni [10,11], Srivastava [2], and Rathie [13].