Some reduction and transformation formulas for the Appell hypergeometric function F2

An integral representation of the Appell series F2(σ,α1,α2;β1,β2;x,y) is used here to obtain several finite-sum expansions in terms of the less cumbersome hypergeometric functions 2F1 and 3F2. In the case when the parameters σ, α1, α2, β1, and β2 are all positive integers, some of our results may be seen as a generalization of the finite-sum expansions of the Appell series F1 obtained by Cuyt et al. [J. Comput. Appl. Math. 5 (1999) 213-219]. Other important consequences (as well as potential applications) of our results are discussed and a listing of some useful reduction (and transformation) formulas is provided.