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hpq-0218

Edited by Hiromasa Nakayama

$  {}_2F_1(x,(-n),w,(- 1 ))=(\frac{(\Gamma(w)\cdot \Gamma(((w-x)+n)))}{(\Gamma(...
... },(-n)),{\tt List}(\frac{( 1 +(x-w-n))}{ 2 },\frac{(( 1 +x)-w-n)}{ 2 }), 1 )) $
Typeset by om2tex.xsl

$ {}_2 F_1 (x,-n,w,-1) = {\frac{\Gamma (w) \Gamma (n + w - x)  {}_pF_q(\{ -n,...
...n}{2}} - {\frac{w}{2}} + {\frac{x}{2}}\} ,1)}{\Gamma (n + w) \Gamma (w - x)}} $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric2F1(x, arith1.unary_minus(n), w,
     arith1.unary_minus(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, x / 2, arith1.unary_minus(n)),
      list1.list(1 + (x - w - n) / 2, (1 + x - w - n) / 2),
      1));

Reversal of "nearly-poised" series

Reference: Retrieve the formula in Mathematica form hpq-0218-math-auto.m Retrieve the formula in Risa/Asir form hpq-0218-asir-auto.rr Retrieve the formula in LaTeX form hpq-0218-tex-auto.tex Interactive replacement hpq-0218-js-auto.html


Nobuki Takayama 2003-02-03