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GeezerVison is showing mathworld.wolfram.com — Regularized Beta Function -- from Wolfram MathWorld

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Regularized Beta Function

The regularized beta function is defined by

I(z;a,b)=(B(z;a,b))/(B(a,b)),

where B(z;a,b) is the incomplete beta function and B(a,b) is the (complete) beta function. The regularized beta function is sometimes also denoted I_z(a,b) and is implemented in the Wolfram Language as BetaRegularized[z, a, b]. The four-argument version BetaRegularized[z1, z2, a, b] is equivalent to I(z_2;a,b)-I(z_1;a,b).

See also

Beta Function, Incomplete Beta Function, Regularized Gamma Function

Related Wolfram sites

https://functions.wolfram.com/GammaBetaErf/BetaRegularized/, https://functions.wolfram.com/GammaBetaErf/BetaRegularized4/

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More things to try:

  • Bailey's theorem
  • Bernoulli B(16)
  • div (x^3 y, y^3 z, z^3 x)

References

Pearson, K. (Ed.). Tables of Incomplete Beta Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1968.

Referenced on Wolfram|Alpha

Regularized Beta Function

Cite this as:

Weisstein, Eric W. "Regularized Beta Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularizedBetaFunction.html

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