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May 18, 2005 - A 3F2 Formula Previous Next

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?

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