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hpq-0206

Edited by Hiromasa Nakayama

$  {}_2F_1(a,b,(k-b),(- 1 ))=(\frac{(\Gamma((k-b))\cdot \Gamma(\frac{k}{ 2 }))}...
...{ 2 })-\frac{a}{ 2 })),{\tt List}((k-a),(\frac{ 1 }{ 2 }+\frac{k}{ 2 })), 1 )) $
Typeset by om2tex.xsl

$ {}_2 F_1 (a,b,-b + k,-1) = {\frac{\Gamma ({\frac{k}{2}}) \Gamma (-b + k)  {...
...1}{2}} + {\frac{k}{2}},-a + k\} ,1)}{\Gamma (-b + {\frac{k}{2}}) \Gamma (k)}} $
Typeset by Mathematica

Formula in the tfb format:

   hypergeo1.hypergeometric2F1(a, b, k - b, arith1.unary_minus(1))
   =
   ((hypergeo0.gamma(k - b) * hypergeo0.gamma(k / 2)) /
     (hypergeo0.gamma(k / 2 - b) * hypergeo0.gamma(k)) * 
    hypergeo1.hypergeometric_pFq(
     list1.list(b, k / 2 - (a / 2), 1 / 2 + (k / 2) - (a / 2)),
     list1.list(k - a, 1 / 2 + (k / 2)),
     1));

Transformation of a nearly-poised series 3 F 2(-1)

Reference: Retrieve the formula in Mathematica form hpq-0206-math-auto.m Retrieve the formula in Risa/Asir form hpq-0206-asir-auto.rr Retrieve the formula in LaTeX form hpq-0206-tex-auto.tex Interactive replacement hpq-0206-js-auto.html


Nobuki Takayama 2003-02-03