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hpq-0211

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Reversal of "nearly-poised" series

Reference: Retrieve the formula in Mathematica form hpq-0211-math-auto.m Retrieve the formula in Risa/Asir form hpq-0211-asir-auto.rr Retrieve the formula in LaTeX form hpq-0211-tex-auto.tex Interactive replacement hpq-0211-js-auto.html


Nobuki Takayama 2003-02-03