2F1[a,a+1,a-1/2,1/4]
Wouter Meeussen
eu000949 at pophost.eunet.be
Fri Jul 14 14:08:00 CEST 2000
is there a 'Well Known Theorem' allowing to generalise
2F1[a,a+1,a-1/2,1/4] for all "a" ?
{Hypergeometric2F1[1, 2, 1/2, 1/4] = 2 + (4*Pi)/(9*Sqrt[3]) },
{Hypergeometric2F1[2, 3, 3/2, 1/4] = 2 + (16*Pi)/(27*Sqrt[3]) },
{Hypergeometric2F1[3, 4, 5/2, 1/4] = 8/3 + (56*Pi)/(81*Sqrt[3]) },
{Hypergeometric2F1[4, 5, 7/2, 1/4] = 10/3 + (80*Pi)/(81*Sqrt[3]) },
{Hypergeometric2F1[5, 6, 9/2, 1/4] = 14/3 + (280*Pi)/(243*Sqrt[3]) },
{Hypergeometric2F1[6, 7, 11/2, 1/4] = 28/5 + (448*Pi)/(243*Sqrt[3]) },
{Hypergeometric2F1[7, 8, 13/2, 1/4] = 44/5 + (1232*Pi)/(729*Sqrt[3]) },
{Hypergeometric2F1[8, 9, 15/2, 1/4] = 286/35 + (9152*Pi)/(2187*Sqrt[3]) },
{Hypergeometric2F1[9, 10, 17/2, 1/4] = 143/7 + (5720*Pi)/(19683*Sqrt[3]) }
(Mathematica 4. has a bit of trouble with it)
wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be
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