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hpq-0208

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Some identities involving hypergeometric series of lower orders

Reference: Retrieve the formula in Mathematica form hpq-0208-math-auto.m Retrieve the formula in Risa/Asir form hpq-0208-asir-auto.rr Retrieve the formula in LaTeX form hpq-0208-tex-auto.tex Interactive replacement hpq-0208-js-auto.html


Nobuki Takayama 2003-02-03