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h21-0036

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

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

$ {}_2 F_1 (a,b,1 + a + b - c,1 - x) = {{
{\tt x}
}^{1 - c}} {}_2 F_1 (1 + b - c,1 + a - c,1 + a + b - c,1 - x) $
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~ (1 ~arith1.minus~ c) ~arith1.times~
      hypergeo1.hypergeometric2F1(b ~arith1.plus~ 1 ~arith1.minus~ c,
        a ~arith1.plus~ 1 ~arith1.minus~ c,
        a ~arith1.plus~ b ~arith1.plus~ 1 ~arith1.minus~ c,
        1 ~arith1.minus~ 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 h21-0036-math-auto.m Retrieve the formula in Risa/Asir form h21-0036-asir-auto.rr Retrieve the formula in LaTeX form h21-0036-tex-auto.tex Interactive replacement h21-0036-js-auto.html


Nobuki Takayama 2003-02-03