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BetaRegularized

BetaRegularized
gives the regularized incomplete beta function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For nonsingular cases, .
  • BetaRegularized gives the generalized regularized incomplete beta function defined in nonsingular cases as Beta[z0, z1, a, b]/Beta[a, b].
  • For certain special arguments, BetaRegularized automatically evaluates to exact values.
Evaluate numerically:
Evaluate numerically:
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Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Series expansion:
TraditionalForm formatting:
Evaluate at integer and half-integer arguments:
Infinite arguments give symbolic results:
BetaRegularized threads element-wise over lists:
BetaRegularized can be applied to power series:
Series expansion at infinity:
Give the result for an arbitrary symbolic direction:
Evaluate at integer and half-integer arguments:
Series expansions at generic points:
Series expansion at infinity:
Plot of the absolute value of BetaRegularized in the complex plane:
Distribution of the average distance of all pairs of points in a -dimensional hypersphere:
Low-dimensional distributions can be expressed in elementary functions:
Plot distributions:
CDF of the Student t distribution:
Plot the CDF for various parameters:
Use FunctionExpand to express through Gamma and Beta functions:
Numerically find a root of a transcendental equation:
Compose with the inverse function:
Use PowerExpand to disregard multivaluedness ambiguity:
Large arguments can give results too large to be computed explicitly:
Machine-number inputs can give high-precision results:
Regularized beta functions are typically not generated by FullSimplify:
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