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Beta Integral

The integral

int_0^1x^p(1-x)^qdx,

called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

See also

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

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References

Gasper, G. "q-Extensions of Barnes', Cauchy's, and Euler's Beta Integrals." In Topics in Mathematical Analysis (Ed. Yh. M. Rassias). London: World Scientific, pp. 194-314, 1989.Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

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Beta Integral

Cite this as:

Weisstein, Eric W. "Beta Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BetaIntegral.html

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