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h21-0037

A relation at x=1 of Kummer's 24 solutions

$  {}_2F_1(a,b,(((a+b)-c)+ 1 ),( 1 -x))=((x)^{(-a)}\cdot  {}_2F_1(((a+ 1 )-c),a,(((a+b)+ 1 )-c),\frac{(x- 1 )}{x})) $
Typeset by om2tex.xsl

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

Formula in the tfb format:

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

A relation at x=1 of Kummer's 24 solutions

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0037-math-auto.m Retrieve the formula in Risa/Asir form h21-0037-asir-auto.rr Retrieve the formula in LaTeX form h21-0037-tex-auto.tex Interactive replacement h21-0037-js-auto.html


Nobuki Takayama 2003-02-03