* Bill Gosper <billgosper@gmail.com> [Aug 05. 2015 07:43]:

http://dlmf.nist.gov/15.8 It seems to need another term on the right. --rwg [...]

Works for me (fixing parameters because of Pari's limitations with symbolic computations): -------------------------------------------- \\ http://dlmf.nist.gov/15.8 \\ eq. 15.8.23 /* \[\mathop{F\/}\nolimits\!\left({a,1-a\atop c};z\right)=\left(\sqrt{1-z^{-1}}-1% \right)^{1-a}\left(\sqrt{1-z^{-1}}+1\right)^{a-2c+1}\left(1-z^{-1}\right)^{c-1% }\mathop{F\/}\nolimits\!\left({c-a,c-\tfrac{1}{2}\atop 2c-1};\frac{4\sqrt{1-z^% {-1}}}{\left(\sqrt{1-z^{-1}}+1\right)^{2}}\right),\] */ \r hypergeom default(echo,1); N=15; z = 1/2/'z^2+O('z^N); c=1 a=1/2 L=hypergeom([a,1-a], [c], z, N) S=sqrt(1-1/z) R = (S-1)^(1-a) * (S+1)^(a-2*c+1) * (1-1/z)^(c-1) R *= hypergeom([c-a, c-1/2], [2*c-1], 4*S/(S+1)^2 , N) L - R quit; -------------------------------------------- The expression 'L - R' near end gives: 93990019574025/147573952589676412928*z^-30 + 25145962430625/18446744073709551616*z^-28 + 1690195005625/576460752303423488*z^-26 + 457028729521/72057594037927936*z^-24 + 7775536041/562949953421312*z^-22 + 2133423721/70368744177664*z^-20 + 147744025/2199023255552*z^-18 + 41409225/274877906944*z^-16 + 184041/536870912*z^-14 + O(z^-13)

DAWK! My bad! The additional term was there, but scrolled off the bottom of my screen! Apologies for the braindamage. --rwg Maybe there should be some sort of typographical "formula hyphen". This could happen at the bottom of the page in an actual book. 18th Century texts duplicated the first line of the next page at the bottom of the current page. Nowadays, we could do that with a miniaturized display. In browsers, too. On Tue, Aug 4, 2015 at 6:31 PM, Bill Gosper <billgosper@gmail.com> wrote:

http://dlmf.nist.gov/15.8 It seems to need another term on the right. --rwg