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h21-0087

$  {}_2F_1(a,b,((a-b)+ 1 ),x)=((( 1 -x))^{(-a)}\cdot  {}_2F_1(\frac{a}{ 2 },\f...
... 1 )-( 2 \cdot b))}{ 2 },((a-b)+ 1 ),\frac{(-( 4 \cdot x))}{(( 1 -x))^{ 2 }})) $
Typeset by om2tex.xsl

$ {}_2 F_1 (a,b,1 + a - b,x) = {\frac{{}_2 F_1 ({\frac{a}{2}},{\frac{1 + a - 2 ...
...4 x}{{{\left( 1 - x \right) }^2}}})}{{{\left( 1 - x \right) }^{
{\tt a}
}}}} $
Typeset by Mathematica

Formula in the tfb format:

    hypergeo1.hypergeometric2F1(a, b, a ~arith1.minus~ b ~arith1.plus~ 1, x)
    ~relation1.eq~
    (arith1.power(1 ~arith1.minus~ x, arith1.unary_minus(a)) 
      ~arith1.times~ hypergeo1.hypergeometric2F1(
         a ~arith1.divide~ 2, 
         (a ~arith1.plus~ 1 ~arith1.minus~ (2 ~arith1.times~ b)) 
~arith1.divide~ 2,
         a ~arith1.minus~ b ~arith1.plus~ 1,
         arith1.unary_minus(4 ~arith1.times~ x) ~arith1.divide~ arith1.power(1 
~arith1.minus~ x, 2)));

Edited by Hiromasa Nakayama

quadratic transformation of independent variable

Reference: Retrieve the formula in Mathematica form h21-0087-math-auto.m Retrieve the formula in Risa/Asir form h21-0087-asir-auto.rr Retrieve the formula in LaTeX form h21-0087-tex-auto.tex Interactive replacement h21-0087-js-auto.html


Nobuki Takayama 2003-02-03