next up previous
Next: hpq-0216 Up: Digital Formula Book for Previous: hpq-0214


hpq-0215

Edited by Hiromasa Nakayama

$  {}_pF_q({\tt List}(x,y,z,(-n)),{\tt List}((( 1 +x)-y),(( 1 +x)-z),w), 1 )=(\...
... +x)-y),(( 1 +x)-z),\frac{( 1 +(x-w-n))}{ 2 },\frac{(( 1 +x)-w-n)}{ 2 }), 1 )) $
Typeset by om2tex.xsl

$  {}_pF_q(\{ -n,x,y,z\} ,\{ w,1 + x - y,1 + x - z\} ,1) = {\frac{\Gamma (w) \...
...}} + {\frac{x}{2}},1 + x - y,1 + x - z\} ,1)}{\Gamma (n + w) \Gamma (w - x)}} $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric_pFq(
     list1.list(x, y, z, arith1.unary_minus(n)),
     list1.list(1 + x - y, 1 + x - z, w),
     1)
    =
    ((hypergeo0.gamma(w) * hypergeo0.gamma(w - x + n))
     /
     (hypergeo0.gamma(w + n) * hypergeo0.gamma(w - x)) 
     *
     hypergeo1.hypergeometric_pFq(
      list1.list(1 + x - w, (1 + x) / 2, x / 2, 1 + x - y - z,
       arith1.unary_minus(n)),
      list1.list(1 + x - y, 1 + x - z, 1 + (x - w - n) / 2, 
       (1 + x - w - n) / 2),
      1));

Reversal of "nearly-poised" series

Reference: Retrieve the formula in Mathematica form hpq-0215-math-auto.m Retrieve the formula in Risa/Asir form hpq-0215-asir-auto.rr Retrieve the formula in LaTeX form hpq-0215-tex-auto.tex Interactive replacement hpq-0215-js-auto.html


Nobuki Takayama 2003-02-03