Could someone be kind enough to independently verify the calculations of the Generalised Hypergeometric Function (Hypergeometric3F2) at
http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=Hypergeometric3F2
With my spreadsheet calculations, I get an opposite sign on the imaginary part of the function outside the unit circle where there is a branch cut. Otherwise both the real part and the absolute value of the imaginary part match the Wolfram calculations to the 9th decimal place
The table below shows my spreadsheet values compared to Wolfram's.
I suspect (but am by no means ready to declare) that there is a local error wherein they use a negative sign instead of a positive one in the sine term of the expansion of $e^{ia_k\pi}$ according to De Moivre's theorem. I have brought this to their attention as well by emailing them directly from the site, but haven't heard from them yet, and don't imagine that I will any time soon.
The transformation for the argument greater than unity that I'm using is
Thanks