next up previous
Next: h21-0032 Up: Digital Formula Book for Previous: h21-0030


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

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

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

Formula in the tfb format:

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

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

Reference: [3, 38-39]

Reference: [4, 64-65] Retrieve the formula in Mathematica form h21-0031-math-auto.m Retrieve the formula in Risa/Asir form h21-0031-asir-auto.rr Retrieve the formula in LaTeX form h21-0031-tex-auto.tex Interactive replacement h21-0031-js-auto.html

Nobuki Takayama 2003-02-03