A novel kind of integral transforms in terms of multiple hypergeometric series and their numerical simulations

In this paper, we introduce a novel class of Hypergeometric function $B_{1}^{\left( n \right)}$ from the investigation of several integral transforms involving the product of Bessel functions and Whittaker functions ${{M}_{k,\xi }}$. Various special cases of our principal results corresponding to the values of the parameters $k$ and $\xi $ of Whittaker function are also derived. Additionally, we carried out some numerical simulations using the Laguerre-Gauss quadrature method and it was demonstrated that the numerical and theoretical predictions are compatible. Therefore, the results presented in this paper can be applied in the theory of mathematical physics such as neutron physics, plasma physics and radio physics.