next up previous
Next: hpq-0015 Up: Digital Formula Book for Previous: hpq-0013


hpq-0014

Edited by Hiromasa Nakayama

$ (( 1 +( 2 \cdot a))=((((b+c)+d)+e)-n) \Rightarrow  {}_pF_q({\tt List}(a,( 1 +...
...mer}
((( 1 +a)-d),n))\cdot
{\tt hypergeo0.pochhammer}
((( 1 +a)-b-c-d),n))}) $
Typeset by om2tex.xsl

$
{\tt implies}
(1 + 2 a = b + c + d + e - n,{\frac{ {}_pF_q(\{ a,b,c,d,e,-n...
...,
{\tt Pochhammer}
(1 + a - d,n) 
{\tt Pochhammer}
(1 + a - b - c - d,n)}}) $
Typeset by Mathematica

Formula in the tfb format:

    logic1.implies(
     (1 + (2 * a)) = (b + c + d + e - n),
     hypergeo1.hypergeometric_pFq(
      list1.list(a, 1 + (a / 2), b, c, d, e, arith1.unary_minus(n)),
      list1.list(a / 2, 1 + a - b, 1 + a - c, 1 + a - d, 1 + a - e,
       1 + a + n),
      1)
     =  
     ((hypergeo0.pochhammer(1 + a, n)
       * hypergeo0.pochhammer(1 + a - b - c, n)
       * hypergeo0.pochhammer(1 + a - b - d, n)
       * hypergeo0.pochhammer(1 + a - c - d, n))
      /
      (hypergeo0.pochhammer(1 + a - b, n)
       * hypergeo0.pochhammer(1 + a - c, n)
       * hypergeo0.pochhammer(1 + a - d, n)
       * hypergeo0.pochhammer(1 + a - b - c - d, n))));

Summation theorems for ordinary hypergeometric series

Reference: Retrieve the formula in Mathematica form hpq-0014-math-auto.m Retrieve the formula in Risa/Asir form hpq-0014-asir-auto.rr Retrieve the formula in LaTeX form hpq-0014-tex-auto.tex Interactive replacement hpq-0014-js-auto.html


Nobuki Takayama 2003-02-03