next up previous
Next: hpq-0205 Up: Digital Formula Book for Previous: hpq-0203


hpq-0204

Edited by Hiromasa Nakayama

$ (
{\tt logic1.or}
(
{\tt set1.in}
((-b),setname1.N),
{\tt logic1.or}
(
{\t...
...Gamma((k-b))\cdot \Gamma((k-c)))\cdot \Gamma((k-d)))\cdot \Gamma((k-b-c-d)))}) $
Typeset by om2tex.xsl

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

Some identities involving hypergeometric series of lower orders

Reference: Retrieve the formula in Mathematica form hpq-0204-math-auto.m Retrieve the formula in Risa/Asir form hpq-0204-asir-auto.rr Retrieve the formula in LaTeX form hpq-0204-tex-auto.tex Interactive replacement hpq-0204-js-auto.html


Nobuki Takayama 2003-02-03