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hpq-0212

Edited by Hiromasa Nakayama

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

$  {}_pF_q(\{ a,b,c,-n\} ,\{ -b + k,-c + k,k + n\} ,1) = {\frac{{{\left( -1 \ri...
...(b) \Gamma (c) \Gamma (-b + k + n) \Gamma (-c + k + n) \Gamma (k + 2 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)
    =
    (arith1.power(arith1.unary_minus(1), n) 
     *
     (hypergeo0.gamma(a + n) * hypergeo0.gamma(b + n) *
      hypergeo0.gamma(c + n) * hypergeo0.gamma(k - b) *
      hypergeo0.gamma(k - c) * hypergeo0.gamma(k + n)) 
     /
     (hypergeo0.gamma(a) * hypergeo0.gamma(b) *
      hypergeo0.gamma(c) * hypergeo0.gamma(k - b + n) *
      hypergeo0.gamma(k - c + n) * hypergeo0.gamma(k + (2 * n))) 
     *
     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));

Reversal of "nearly-poised" series

Reference: Retrieve the formula in Mathematica form hpq-0212-math-auto.m Retrieve the formula in Risa/Asir form hpq-0212-asir-auto.rr Retrieve the formula in LaTeX form hpq-0212-tex-auto.tex Interactive replacement hpq-0212-js-auto.html


Nobuki Takayama 2003-02-03