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hpq-0007

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0007-math-auto.m Retrieve the formula in Risa/Asir form hpq-0007-asir-auto.rr Retrieve the formula in LaTeX form hpq-0007-tex-auto.tex Interactive replacement hpq-0007-js-auto.html


Nobuki Takayama 2003-02-03