Abstract: “Generating functions play a very important role in most of the Mathematical and statistical problems. The present study has derived and discussed the addition theorem of special functions whose generating function is exponential. The code of the derivative is also discussed. Exponential generating functions and other special functions have high importance in addition theorem, applicable in various recently developing fields like Computational electro-magnetic fields and other computational fields. It works by automatization in Fast Multi-pole Method using Singular Value Decomposition (SVD). Its code can be applied using Mathematica, Matlab and other software packages.”

Keywords: Generating functions, addition theorem, automatization