WDS> On 3/12/14, Warren D Smith <warren.wds@gmail.com> wrote: Of course 4F3(x) and indeed any pFq(x) with p<=q+1, is defined for all complex x except for a set of measure zero, via analytic continuation. And this particular 4F3 is of course an algebraic function which makes that obvious. --and http://functions.wolfram.com/HypergeometricFunctions/HypergeometricPFQ/ gives explicit formulas such as integral representations. Pade and Borel summation should also work. <wds For more ideas, this ancient Macsyma Newsletter: http://gosper.org/newsrope.pdf (which, of course, isn't restricted to quintics.) --rwg Mma's InverseSeries should be able to do some of this. Then FindSequenceFunction of a bleepload of terms might give you some interesting identities.