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hpq-0012

Edited by Hiromasa Nakayama

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

$ {\frac{ {}_pF_q(\{ a,b,c,d\} ,\{ 1 + a - b,1 + a - c,1 + a - d\} ,1) + 3 a ...
...+ a) \Gamma (1 + a - b - c) \Gamma (1 + a - b - d) \Gamma (1 + a - c - d)}} $
Typeset by Mathematica

Formula in the tfb format:

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

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0012-math-auto.m Retrieve the formula in Risa/Asir form hpq-0012-asir-auto.rr Retrieve the formula in LaTeX form hpq-0012-tex-auto.tex Interactive replacement hpq-0012-js-auto.html


Nobuki Takayama 2003-02-03