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h21-0032

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

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

Formula in the tfb format:

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

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

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0032-math-auto.m Retrieve the formula in Risa/Asir form h21-0032-asir-auto.rr Retrieve the formula in LaTeX form h21-0032-tex-auto.tex Interactive replacement h21-0032-js-auto.html


Nobuki Takayama 2003-02-03