BetaRegularized

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: