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.  2004 Elsevier Inc. All rights reserved.