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hpq-0205

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Some identities involving hypergeometric series of lower orders

Reference: Retrieve the formula in Mathematica form hpq-0205-math-auto.m Retrieve the formula in Risa/Asir form hpq-0205-asir-auto.rr Retrieve the formula in LaTeX form hpq-0205-tex-auto.tex Interactive replacement hpq-0205-js-auto.html


Nobuki Takayama 2003-02-03