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hpq-0009

Edited by Hiromasa Nakayama

$  {}_pF_q({\tt List}(a,b,(-n)),{\tt List}((( 1 +a)-b),(( 1 +a)+n), 1 ), 1 )=\f...
...r}
(( 1 +\frac{a}{ 2 }),n)\cdot
{\tt hypergeo0.pochhammer}
((( 1 +a)-b),n))} $
Typeset by om2tex.xsl

$  {}_pF_q(\{ a,b,-n\} ,\{ 1,1 + a - b,1 + a + n\} ,1) = {\frac{
{\tt Pochhamm...
...}{
{\tt Pochhammer}
(1 + {\frac{a}{2}},n) 
{\tt Pochhammer}
(1 + a - b,n)}} $
Typeset by Mathematica

Formula in the tfb format:

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

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0009-math-auto.m Retrieve the formula in Risa/Asir form hpq-0009-asir-auto.rr Retrieve the formula in LaTeX form hpq-0009-tex-auto.tex Interactive replacement hpq-0009-js-auto.html


Nobuki Takayama 2003-02-03