I was writing functions to check arguments against convergence conditions for 3F2 and most of it is obvious, except:
- some sources state that if the denominator parameters are negative integers the function (or just the power series) is undefined
- Mathematica will happily calculate these functions with negative integers in the denominator and it returns as the answer the series all the way up to the term before the undefined term.
Currently as written I left it at #2 and added tests comparing our values to Mathematica (which does use continuation and various other tricks). Any more informed opinions or better reference sources? I imagine this is one of those situations where there is a continuation but the power series is clearly undefined.