Recursion formulas for Appell's hypergeometric function \(F_2\) with some applications to radiation field problems
A number of interesting new recursion formulae for the Appell functions \(F_2(\sigma,\alpha_1\alpha_2\pm n;\beta_1, \beta_2; x,y)\) and \(F_2(\sigma,\alpha_1 \alpha_2; \beta_1, \beta_2\pm n; x,y)\), where \(n\in N_0= \{0,11,2,\dots\}\), are derived by using some contiguous function relations for the Gauss hypergeometric series \(_2F_1\). The authors discuss applications of their results to the evaluation of radiation field integrals. A number of new reduction formulae is also established. Using these formulas, a number of numerical identities of multiple hypergeometric functions is also derived.
scientific article; zbMATH DE number 5518812