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hpq-0213

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Reversal of "nearly-poised" series

Reference: Retrieve the formula in Mathematica form hpq-0213-math-auto.m Retrieve the formula in Risa/Asir form hpq-0213-asir-auto.rr Retrieve the formula in LaTeX form hpq-0213-tex-auto.tex Interactive replacement hpq-0213-js-auto.html


Nobuki Takayama 2003-02-03