Recursion formulas for Appell’s hypergeometric function F2 with some applications to radiation field problems
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摘要
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.
论文关键词：Multiple hypergeometric functions,Appell functions,Recursion formulas,Integral representations,Gauss hypergeometric function,Generalized hypergeometric series,Reduction and transformation formulas,Contiguous function relations,Radiation field integrals,Applications and numerical results
论文评审过程：Available online 17 November 2008.
论文官网地址：https://doi.org/10.1016/j.amc.2008.11.006
