# 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

```