Multiplication theorems for multi-variable and multi-index Bessel functions

Abstract

In this article, we derive multiplication theorems for the 3-variable 2-parameter Bessel functions $J_n(\lambda x,\mu y,\nu z;\tau_1,\tau_2)$ and 2-index 5-variable 3-parameter Bessel functions $J_{m,n}(\lambda x,\mu y,\nu z,\eta w,\beta h;\tau_1,\tau_2,\tau_3)$ using the generating function method. Further, we derive multiplication theorems for functions related to $J_n(\lambda x,\mu y,\nu z;\tau_1,\tau_2)$ and $J_{m,n}(\lambda x,\mu y,\nu z,\eta w,\beta h;\tau_1,\tau_2,\tau_3)$. Furthermore, we establish a multiplication theorem for N-index Bessel functions $J_{m_1,m_2.....m_N}(\lambda x)$.