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h21-0060

$ (\frac{\frac{(( 2 \cdot {}^ 2 \sqrt{\pi})\cdot \Gamma(((a+b)+\frac{ 1 }{ 2 }))...
...dot a),( 2 \cdot b),((a+b)+\frac{ 1 }{ 2 }),\frac{( 1 -{}^ 2 \sqrt{x})}{ 2 })) $
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$ {\frac{2 {\sqrt{\pi }} \Gamma ({\frac{1}{2}} + a + b) {}_2 F_1 (a,b,{\frac{...
...}{2}}) + {}_2 F_1 (2 a,2 b,{\frac{1}{2}} + a + b,{\frac{1 + {\sqrt{x}}}{2}}) $
Typeset by Mathematica

Formula in the tfb format:

    2 ~arith1.times~ arith1.root(nums1.pi,2)
      ~arith1.times~ hypergeo0.gamma(a ~arith1.plus~ b ~arith1.plus~
        (1 ~arith1.divide~ 2))
      ~arith1.divide~ hypergeo0.gamma(a ~arith1.plus~ (1 ~arith1.divide~ 2))
      ~arith1.divide~ hypergeo0.gamma(b ~arith1.plus~ (1 ~arith1.divide~ 2))
      ~arith1.times~ hypergeo1.hypergeometric2F1(a,b,1 ~arith1.divide~ 2,x)
    ~relation1.eq~
    (hypergeo1.hypergeometric2F1(2 ~arith1.times~ a, 2 ~arith1.times~ b,
      a ~arith1.plus~ b ~arith1.plus~ (1 ~arith1.divide~ 2),
      1 ~arith1.plus~ arith1.root(x,2) ~arith1.divide~ 2)
      ~arith1.plus~
      hypergeo1.hypergeometric2F1(2 ~arith1.times~ a, 2 ~arith1.times~ b,
        a ~arith1.plus~ b ~arith1.plus~ (1 ~arith1.divide~ 2),
        1 ~arith1.minus~ arith1.root(x,2) ~arith1.divide~ 2));

Edited by Yasushi Tamura

Quadratic transformation of independent variable

Reference: Retrieve the formula in Mathematica form h21-0060-math-auto.m Retrieve the formula in Risa/Asir form h21-0060-asir-auto.rr Retrieve the formula in LaTeX form h21-0060-tex-auto.tex Interactive replacement h21-0060-js-auto.html


Nobuki Takayama 2003-02-03