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h21-0044

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}))=((((-x...
...-a- 1 )})\cdot  {}_2F_1(((a+ 1 )-c),( 1 -b),((a+ 1 )-b),\frac{ 1 }{( 1 -x)})) $
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$ {\frac{{}_2 F_1 (a,1 + a - c,1 + a - b,{\frac{1}{x}})}{{{\left( -
{\tt x}
\r...
... -x \right) }^{1 - c}} {}_2 F_1 (1 + a - c,1 - b,1 + a - b,{\frac{1}{1 - x}}) $
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~
    (arith1.unary_minus(x) ~arith1.power~ (1 ~arith1.minus~ c) ~arith1.times~
      ((1 ~arith1.minus~ x) ~arith1.power~
        (c ~arith1.minus~ a ~arith1.minus~ 1)) ~arith1.times~
      hypergeo1.hypergeometric2F1(a ~arith1.plus~ 1 ~arith1.minus~ c,
        1 ~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 h21-0044-math-auto.m Retrieve the formula in Risa/Asir form h21-0044-asir-auto.rr Retrieve the formula in LaTeX form h21-0044-tex-auto.tex Interactive replacement h21-0044-js-auto.html


Nobuki Takayama 2003-02-03