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Eulerian Integral of the Second Kind


For R[n]>-1 and R[z]>0,

Pi(z,n)=n^zint_0^1(1-x)^nx^(z-1)dx
(1)
=(n!)/((z)_(n+1))n^z
(2)
=B(z,n+1),
(3)

where (z)_n is the Pochhammer symbol and B(p,q) is the beta function.


See also

Beta Function, Beta Integral, Eulerian Integral of the First Kind

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Cite this as:

Weisstein, Eric W. "Eulerian Integral of the Second Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerianIntegraloftheSecondKind.html

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