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hpq-0002

Edited by Hiromasa Nakayama

$ ((c+d)=(((a+b)-n)+ 1 ) \Rightarrow  {}_pF_q({\tt List}(a,b,(-n)),{\tt List}(c...
... {\tt hypergeo0.pochhammer}
(c,n)}}{
{\tt hypergeo0.pochhammer}
((c-a-b),n)}) $
Typeset by om2tex.xsl

$
{\tt implies}
(c + d = 1 + a + b - n, {}_pF_q(\{ a,b,-n\} ,\{ c,d\} ,1) = {...
...er}
(-b + c,n)}{
{\tt Pochhammer}
(c,n) 
{\tt Pochhammer}
(-a - b + c,n)}}) $
Typeset by Mathematica

Formula in the tfb format:

    logic1.implies(
      (c ~arith1.plus~ d) ~relation1.eq~ 
        (a ~arith1.plus~ b ~arith1.minus~ n ~arith1.plus~ 1),
      hypergeo1.hypergeometric_pFq(
        list1.list(a, b, arith1.unary_minus(n)),
        list1.list(c, d),
        1)
        ~relation1.eq~
        (hypergeo0.pochhammer(c ~arith1.minus~ a, n) ~arith1.times~
        hypergeo0.pochhammer(c ~arith1.minus~ b, n) ~arith1.divide~
        hypergeo0.pochhammer(c, n) ~arith1.divide~
        hypergeo0.pochhammer(c ~arith1.minus~ a ~arith1.minus~ b, n)));

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0002-math-auto.m Retrieve the formula in Risa/Asir form hpq-0002-asir-auto.rr Retrieve the formula in LaTeX form hpq-0002-tex-auto.tex Interactive replacement hpq-0002-js-auto.html


Nobuki Takayama 2003-02-03