Title: Some expansions of hypergeometric functions in series of hypergeometric functions
Abstract: Throughout the present note we abbreviate the set of p parameters a 1 ,…, a p by ( a p ), with similar interpretations for ( b q ), etc. Also, by [( a p )] m we mean the product , where [λ] m = Г(λ + m)/ Г(λ) , and so on. One of the main results we give here is the expansion formula (1) which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative integers such that p+r < q+s+l (or p+r = q+s+l and |zω| <1), p+t < q+u (or p + t = q + u and |z| < 1) , and the various parameters including μ are so restricted that each side of equation (1) has a meaning.