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h21-0033

A relation at x=0 of Kummer's 24 solutions

$ ((x)^{( 1 -c)}\cdot  {}_2F_1(((a-c)+ 1 ),((b-c)+ 1 ),( 2 -c),x))=(((x)^{( 1 -c)}\cdot (( 1 -x))^{(c-a-b)})\cdot  {}_2F_1(( 1 -a),( 1 -b),( 2 -c),x)) $
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$ {x^{1 - c}} {}_2 F_1 (1 + a - c,1 + b - c,2 - c,x) = {{\left( 1 - x \right) }^{-a - b + c}} {x^{1 - c}} {}_2 F_1 (1 - a,1 - b,2 - c,x) $
Typeset by Mathematica

Formula in the tfb format:

    x ~arith1.power~ (1 ~arith1.minus~ c) ~arith1.times~
    hypergeo1.hypergeometric2F1(a ~arith1.minus~ c ~arith1.plus~ 1,
      b ~arith1.minus~ c ~arith1.plus~ 1, 2 ~arith1.minus~ c,x) ~relation1.eq~
    ( x ~arith1.power~ (1 ~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~ a, 1 ~arith1.minus~ b,
        2 ~arith1.minus~ c, x));

A relation at x=0 of Kummer's 24 solutions

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0033-math-auto.m Retrieve the formula in Risa/Asir form h21-0033-asir-auto.rr Retrieve the formula in LaTeX form h21-0033-tex-auto.tex Interactive replacement h21-0033-js-auto.html


Nobuki Takayama 2003-02-03