Recursion formulas for Appell's hypergeometric function F2 with some applications to radiation field problems

Using some contiguous function relations for the classical Gauss hypergeometric series 2F1, we establish a number of new recursion formulas for the Appell functionsF2(σ,α1,α2±n;β1,β2;x,y)andF2(σ,α1,α2;β1,β2±n;x,y),wheren∈N0≔{0,1,2,…}=N∪{0}.Some important applications of our results to the evaluation of radiation field integrals are discussed and a listing of some useful reduction (and transformation) formulas is provided.