Date: 2017-02-19 00:30 From: Joerg Arndt <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com> Just put a 1 into the upper parameters to cancel that lower hidden 1: (arcsin(z))^2 = z^2 * F([1, 1, 1], [3/2, 2], z^2) At least that's what my notes say (fxtbook, p.700). Best regards, jj Sorry, I was too cryptic. I was simply asking where this is in DLMF. It "belongs" in http://dlmf.nist.gov/15.4, but that bogus 1 disqualifies it. Look how trivial it is as a product matrix: 2 2 k z 1 ------- - 1 + 2 k k 0 1 But it doesn't have the obligatory k+1 in the 1,1 denominator. So it gets shunned. --rwg * Bill Gosper <billgosper@gmail.com> [Feb 19. 2017 08:50]:

I just fixed an egregious paste-o in gosper.org/pathi.pdf giving a second, spurious value for ζ(2,¼) instead of the intended ζ(2,¾), leading to an absurd "closed form" for Catalan's constant. --rwg (I also wasted > ½ an hr trying to figure out why the new pdf didn't replace the old one at gosper.org. Eventually it did.)

DLMF question: Due to the braindead hidden 1 in ₂F₁ notation, it can't express arcsin². So where in DLMF is the ₃F₂?