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hpq-0214

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

    hypergeo1.hypergeometric_pFq(
     list1.list(1 - (2 * n) - k, 1 - n - k + b, 1 - n - k + c,
      arith1.unary_minus(n)),
     list1.list(1 - n - b, 1 - n - c, 1 - n - a),
     1)
    =
     ((hypergeo0.gamma(1 - n - a) * hypergeo0.gamma(k - a + (2 * n)))
     /
     (hypergeo0.gamma(1 - a) * hypergeo0.gamma(k - a + n)) 
     *
     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-0214-math-auto.m Retrieve the formula in Risa/Asir form hpq-0214-asir-auto.rr Retrieve the formula in LaTeX form hpq-0214-tex-auto.tex Interactive replacement hpq-0214-js-auto.html


Nobuki Takayama 2003-02-03