wds> Gosper has an annoying habit of using non-ASCII characters I cannot read, which come out as "?" on my screen. Or maybe they really are "?". Who knows? hmm, that might explain why I'm not getting any answers. Off list I've been merrily exchanging emails with Chinese and all sorts of exotica from the Special Characters menu. But this time the culprit is not math-fun--I can see the Uppercase Gamma in my Subject summary window, where there's a ? in Warren's reply. Who else is having this problem? Was anybody besides Warren pwned by my BLACK RIGHT-POINTING SMALL TRIANGLE (▸), (which GMail has suddenly stopped inserting on double-clicking the font table)? Maybe Warren is alone on a network made of juice cans and string? Anyway, he's right. I should've stipulated 0<k<n under the product. But he might have guessed my intent from the n=12 example, which is plain ASCII, except for the pi. Haven't we been using π quite a while now? It's just option p on the Mac keyboard. --rwg On Fri, Jan 18, 2013 at 3:39 PM, Bill Gosper <billgosper@gmail.com> wrote:
Someone once sent me (us?) a paper deriving (presumably by inclusion-exclusion) this gamma product formula. Does anyone remember where it is? Presumably for n=12 it gives something like
(z - 11/12)!*(z - 7/12)!*(z - 5/12)!*(z - 1/12)!== 4*(2*z)!*(12*z)!*π^2/(2^(12*z)*3^(6*z)*(4*z)!*(6*z)!)
It doesn't seem to be on http://functions.wolfram.com/ --rwg