next up previous
Next: hpq-0011 Up: Digital Formula Book for Previous: hpq-0009


hpq-0010

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

    hypergeo1.hypergeometric_pFq(
     list1.list(a, 1 + (a / 2), b, c),
     list1.list(a / 2, 1 + a - b, 1 + a - c),
     arith1.unary_minus(1))
    =
    ((hypergeo0.gamma(1 + a - b) 
      * hypergeo0.gamma(1 + a - c))
     /
     (hypergeo0.gamma(1 + a)
      * hypergeo0.gamma(1 + a - b - c)));

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0010-math-auto.m Retrieve the formula in Risa/Asir form hpq-0010-asir-auto.rr Retrieve the formula in LaTeX form hpq-0010-tex-auto.tex Interactive replacement hpq-0010-js-auto.html


Nobuki Takayama 2003-02-03