An integral representation of some hypergeometric functions

The Euler integral representation of the F-2(1) Gauss hypergeometric function is well known and plays a prominent role in the derivation of transformation identities and in the evaluation of F-2(1)(a,b;c;1), among other applications. The general F-p+k(q+k) hypergeometric function has an integral representation where the integrand involves F-p(q). We give a simple and direct proof of an Euler integral representation for a special class of F-q+1(q) functions for q >= 2. The values of certain F-3(2) and F-4(3) functions at x = 1, some of which can be derived using other methods, are deduced from our integral formula.