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h21-0042

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

$ {\frac{{}_2 F_1 (a,1 + a - c,1 + a - b,{\frac{1}{x}})}{{{\left( -
{\tt x}
\r...
...{\left( -x \right) }^{b - c}} {}_2 F_1 (1 - b,-b + c,1 + a - b,{\frac{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~ (b ~arith1.minus~ c) ~arith1.times~
      ((1 ~arith1.minus~ x) ~arith1.power~
        (c ~arith1.minus~ a ~arith1.minus~ b)) ~arith1.times~
      hypergeo1.hypergeometric2F1(1 ~arith1.minus~ b, c ~arith1.minus~ b,
        a ~arith1.plus~ 1 ~arith1.minus~ b, 1 ~arith1.divide~ 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 h21-0042-math-auto.m Retrieve the formula in Risa/Asir form h21-0042-asir-auto.rr Retrieve the formula in LaTeX form h21-0042-tex-auto.tex Interactive replacement h21-0042-js-auto.html


Nobuki Takayama 2003-02-03