Euler Integral

1. Euler integral of the first kind: the Beta function
   $\backslash Beta(x,y)=\; \backslash int\_0^1t^\{x-1\}(1-t)^\{y-1\}\backslash ,dt\; =\backslash frac\{\backslash Gamma(x)\backslash Gamma(y)\}\{\backslash Gamma(x+y)\}$
2. Euler integral of the second kind: the Gamma function
   $$

$\backslash Beta(n,m)=\; \{(n-1)!(m-1)!\; \backslash over\; (n+m-1)!\}=\{n+m\; \backslash over\; nm\{n+m\; \backslash choose\; n\}\}$

$\backslash Gamma(n)\; =\; (n-1)!\; \backslash ,$

See also

• Leonhard Euler

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