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h21-0043

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

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

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

Formula in the tfb format:

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

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

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0043-math-auto.m Retrieve the formula in Risa/Asir form h21-0043-asir-auto.rr Retrieve the formula in LaTeX form h21-0043-tex-auto.tex Interactive replacement h21-0043-js-auto.html


Nobuki Takayama 2003-02-03