On 2/17/2012 3:25 PM, Bill Gosper wrote:
We really need a repository of such results. (It's probably in BHS, but I can never find anything in there w/o help from George or Mizan.) Presumably, q-holonomy is at or near the point of automatically proving these, but what if you only have one side of the eqn, and wonder what other forms are known?
Even if Mma's Sum is disciplined by FunctionExpand, the latter is already overloaded and underspecific.
There's a surprising wealth of stuff in DLMF chap 17 (including four identities by Fine). Could this somehow be sufficiently aggrandized? It has a fairly lame assortment of contiguity relations, but the right way to do these is with matrices. But matrices are impractical w/o an underlying math engine. I.e., we need a "live DLMF". Maybe someday in Mma.
For a while now, I've been thinking about building a live database of formulas, with some backend with a math engine. In fact, probably a year ago, I started building it. But then I realized that I, alone, probably wouldn't have the patience to digitize most of the A&S or DLMF or etc. formulas in S-exp syntax. Maybe if there's interest, I'll resume work on it again! -Robert