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hpq-0200

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Transformation of a nearly-poised series 3 F 2(-1)

Reference: Retrieve the formula in Mathematica form hpq-0200-math-auto.m Retrieve the formula in Risa/Asir form hpq-0200-asir-auto.rr Retrieve the formula in LaTeX form hpq-0200-tex-auto.tex Interactive replacement hpq-0200-js-auto.html


Nobuki Takayama 2003-02-03