
I added a search engine to PLANETQUANTUM.COM and I made the Quantum Manual look just a bit more modern, which was desperately needed. I'm warming up my integration code (Risch, MeijerG, etc.). There is an interesting 3F2 formula in PBM volume 3 which I stumbled upon:
There was no clue where this came from. After 3 days of various guesswork and numerical experiments, I came up with this general formula:
I haven't proven it, I just believe it is true. I would be happy to know a reference for this curiosity. There are fascinating 2F1(a1,a2;b1;c) formulas for various rational numbers c. I've been searching for them to find formulas like these:
It would be really great to add formulas like these to my 100,000+ hypergeometric formulas database, wouldn't it?

©20042024 Planet Quantum  Kelly Roach 