Euler integral

Euler integral

In mathematics, there are two types of Euler integral:
#"Euler integral of the first kind": the Beta function
mathrm{Beta}(x,y)= int_0^1t^{x-1}(1-t)^{y-1},dt =frac{Gamma(x)Gamma(y)}{Gamma(x+y)}
#"Euler integral of the second kind": the Gamma function
Gamma(z) = int_0^infty t^{z-1},e^{-t},dt

For positive integers "m" and "n":mathrm{Beta}(n,m)= {(n-1)!(m-1)! over (n+m-1)!}={n+m over nm{n+m choose n:Gamma(n) = (n-1)! ,

ee also

*Leonhard Euler
*Euler function (disambiguation)


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