next up previous
Next: hpq-0202 Up: Digital Formula Book for Previous: hpq-0200


hpq-0201

Edited by Hiromasa Nakayama

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

$
{\tt implies}
(
{\tt logic1Or}
(
{\tt set1In}
(-b,
{\tt setname1N}
),
{\...
...}{\Gamma (k) \Gamma (-b - c + k) \Gamma (-b - d + k) \Gamma (-c - d + k)}}) $
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(k - b, k - c, k - d), 1)
    =
    ((hypergeo0.gamma(k - b) * hypergeo0.gamma(k - c) * 
      hypergeo0.gamma(k - d) * hypergeo0.gamma(k - b - c - d)) 
     /
     (hypergeo0.gamma(k - c - d) * hypergeo0.gamma(k - b - c) *
      hypergeo0.gamma(k - b - d) * hypergeo0.gamma(k)) 
     * 
     hypergeo1.hypergeometric_pFq(
      list1.list(b, c, d, k / 2 - (a / 2), 1 / 2 + (k / 2) - (a / 2)),
      list1.list(k - a, k / 2, 1 / 2 + (k / 2), b + c + d - k + 1),
      1)));

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

Reference: Retrieve the formula in Mathematica form hpq-0201-math-auto.m Retrieve the formula in Risa/Asir form hpq-0201-asir-auto.rr Retrieve the formula in LaTeX form hpq-0201-tex-auto.tex Interactive replacement hpq-0201-js-auto.html


Nobuki Takayama 2003-02-03