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hpq-0203

Edited by Hiromasa Nakayama

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

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

Formula in the tfb format:

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

Transformation of a nearly-poised series 4 F 3(1)

Reference: Retrieve the formula in Mathematica form hpq-0203-math-auto.m Retrieve the formula in Risa/Asir form hpq-0203-asir-auto.rr Retrieve the formula in LaTeX form hpq-0203-tex-auto.tex Interactive replacement hpq-0203-js-auto.html


Nobuki Takayama 2003-02-03