next up previous
Next: h32-0300 Up: Digital Formula Book for Previous: h21-0300


h32-0001

Saalschutz identity

$ (
{\tt set1.in}
(n,
{\tt interval1.integer_interval}
( 1 ,nums1.infinity)) \...
...t hypergeo0.pochhammer}
(c,n)\cdot
{\tt hypergeo0.pochhammer}
((c-a-b),n))}) $
Typeset by om2tex.xsl

$
{\tt implies}
(
{\tt set1In}
(n,
{\tt interval1IntegerInterval}
(1,\infty)...
...er}
(-b + c,n)}{
{\tt Pochhammer}
(c,n) 
{\tt Pochhammer}
(-a - b + c,n)}}) $
Typeset by Mathematica

Formula in the tfb format:

   logic1.implies(n ~set1.in~
       interval1.integer_interval(1,nums1.infinity),
     hypergeo1.hypergeometric_pFq(
        list1.list(a,b,arith1.unary_minus(n)),
        list1.list(c,a ~arith1.plus~ b ~arith1.minus~ n ~arith1.plus~ 1 
~arith1.minus~ c),
        1) ~relation1.eq~
     (hypergeo0.pochhammer(c ~arith1.minus~ a, n) ~arith1.times~
      hypergeo0.pochhammer(c ~arith1.minus~ b, n) ~arith1.divide~ 
     (hypergeo0.pochhammer(c, n) ~arith1.times~
      hypergeo0.pochhammer(c ~arith1.minus~ a ~arith1.minus~ b,n))));

Edited by Nobuki Takayama

Saalschutz identity is a formula on the value at 1.

Reference: Retrieve the formula in Mathematica form h32-0001-math-auto.m Retrieve the formula in Risa/Asir form h32-0001-asir-auto.rr Retrieve the formula in LaTeX form h32-0001-tex-auto.tex Interactive replacement h32-0001-js-auto.html


Nobuki Takayama 2003-02-03