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hpq-0008

Edited by Hiromasa Nakayama

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

$  {}_pF_q(\{ a,b,c\} ,\{ 1,1 + a - b,1 + a - c\} ,1) = {\frac{\Gamma (1 + {\fr...
...+ {\frac{a}{2}} - b) \Gamma (1 + {\frac{a}{2}} - c) \Gamma (1 + a - b - c)}} $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric_pFq(
     list1.list(a, b, c), 
     list1.list(1 + a - b, 1 + a - c, 1),
     1)
    =
    ((hypergeo0.gamma(1 + (a / 2)) 
      * hypergeo0.gamma(1 + a - b)
      * hypergeo0.gamma(1 + a - c)
      * hypergeo0.gamma(1 + (a / 2) - b - c))
      /
      (hypergeo0.gamma(1 + a)
       * hypergeo0.gamma(1 + (a / 2) - b)
       * hypergeo0.gamma(1 + (a / 2) - c)
       * hypergeo0.gamma(1 + a - b - c)) );

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0008-math-auto.m Retrieve the formula in Risa/Asir form hpq-0008-asir-auto.rr Retrieve the formula in LaTeX form hpq-0008-tex-auto.tex Interactive replacement hpq-0008-js-auto.html


Nobuki Takayama 2003-02-03