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Title: Regularized Beta Function -- from Wolfram MathWorld

Open Graph Title: Regularized Beta Function -- from Wolfram MathWorld

X Title: Regularized Beta Function -- from Wolfram MathWorld

Description: 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).

Open Graph Description: 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).

X Description: 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).

Opengraph URL: https://mathworld.wolfram.com/RegularizedBetaFunction.html

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DC.TitleRegularized Beta Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionThe 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).
DC.Subject33B15
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/RegularizedBetaFunction.html
DC.Languageen
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