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hpq-0202

Edited by Hiromasa Nakayama

$ (
{\tt logic1.or}
(
{\tt set1.in}
((-b),setname1.N),
{\tt logic1.or}
(
{\t...
...ist}(( 1 +\frac{a}{ 2 }),(\frac{ 1 }{ 2 }+\frac{a}{ 2 }),(((b+c)+d)-a)), 1 ))) $
Typeset by om2tex.xsl

$
{\tt implies}
(
{\tt logic1Or}
(
{\tt set1In}
(-b,
{\tt setname1N}
),
{\...
... a) \Gamma (1 + a - b - c) \Gamma (1 + a - b - d) \Gamma (1 + a - c - d)}}) $
Typeset by Mathematica

Formula in the tfb format:

   logic1.implies(
    logic1.or(set1.in(arith1.unary_minus(b), setname1.N), 
     logic1.or(set1.in(arith1.unary_minus(c), setname1.N), 
      set1.in(arith1.unary_minus(d), setname1.N))),
    hypergeo1.hypergeometric_pFq(list1.list(a, b, c, d),
     list1.list(1 + a - b,  1 + a - c, 1 + a - d), 1)
    =
    ((hypergeo0.gamma(1 + a - b) * hypergeo0.gamma(1 + a - c) * 
      hypergeo0.gamma(1 + a - d) * hypergeo0.gamma(1 + a - b - c - d)) 
     /
     (hypergeo0.gamma(1 + a - c - d) * hypergeo0.gamma(1 + a - b - c) *
      hypergeo0.gamma(1 + a - b - d) * hypergeo0.gamma(1 + a)) 
     * 
     hypergeo1.hypergeometric_pFq(
      list1.list(1 / 2, b, c, d),
      list1.list(1 + (a / 2), 1 / 2 + (a / 2), b + c + d - a),
      1)));

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

Reference: Retrieve the formula in Mathematica form hpq-0202-math-auto.m Retrieve the formula in Risa/Asir form hpq-0202-asir-auto.rr Retrieve the formula in LaTeX form hpq-0202-tex-auto.tex Interactive replacement hpq-0202-js-auto.html


Nobuki Takayama 2003-02-03