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hpq-0005

Edited by Hiromasa Nakayama

$  {}_2F_1(a,b,(( 1 +a)-b),(- 1 ))=\frac{(\Gamma((( 1 +a)-b))\cdot \Gamma(( 1 +\frac{a}{ 2 })))}{(\Gamma(( 1 +a))\cdot \Gamma((( 1 +\frac{a}{ 2 })-b)))} $
Typeset by om2tex.xsl

$ {\frac{{\sqrt{\pi }} \Gamma (1 + a - b)}{{2^a} \Gamma ({\frac{1}{2}} + {\fra...
...{a}{2}}) \Gamma (1 + a - b)}{\Gamma (1 + a) \Gamma (1 + {\frac{a}{2}} - b)}} $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric2F1(a, b, 1 + a - b, arith1.unary_minus(1))
    =
    ((hypergeo0.gamma(1 + a - b) * hypergeo0.gamma(1 + (a / 2)))
     /
     (hypergeo0.gamma(1 + a) * hypergeo0.gamma(1 + (a / 2) - b)));

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0005-math-auto.m Retrieve the formula in Risa/Asir form hpq-0005-asir-auto.rr Retrieve the formula in LaTeX form hpq-0005-tex-auto.tex Interactive replacement hpq-0005-js-auto.html


Nobuki Takayama 2003-02-03