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h21-0030

A relation at x=0 of Kummer's 24 solutions

$  {}_2F_1(a,b,c,x)=((( 1 -x))^{(c-a-b)}\cdot  {}_2F_1((c-a),(c-b),c,x)) $
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$ {}_2 F_1 (a,b,c,x) = {{\left( 1 - x \right) }^{-
{\tt a}
- b +
{\tt c}
}} {}_2 F_1 (-a + c,-b + c,c,x) $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric2F1(a,b,c,x) ~relation1.eq~
    ( (1 ~arith1.minus~ x) ~arith1.power~
      (c ~arith1.minus~ a ~arith1.minus~ b)
    ~arith1.times~
    hypergeo1.hypergeometric2F1(c ~arith1.minus~ a, c ~arith1.minus~ b, c, x));

A relation at x=0 of Kummer's 24 solutions

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0030-math-auto.m Retrieve the formula in Risa/Asir form h21-0030-asir-auto.rr Retrieve the formula in LaTeX form h21-0030-tex-auto.tex Interactive replacement h21-0030-js-auto.html


Nobuki Takayama 2003-02-03