Beta Function Calculator

Online calculator and formulas for computing the Beta function Β(a,b)

Beta Function Calculator

Beta Function

The calculator computes the Beta function B(a,b) for two positive parameters a and b.

Positive value for parameter a
Positive value for parameter b
Result
B(a,b):

Beta Function Visualization


Beta Function

Graphical representation of the Beta function for various parameters a and b.

Beta Function Formulas

Integral Representation
Beta Function Integral
Alternative Representation
Beta Function Alternative

Gamma Relation

Relation to Gamma Function
Beta Gamma Relation

The Beta function can be expressed as the ratio of Gamma functions.

Description of the Beta Function

Mathematical Definition

The calculator on this page computes the Beta function B(a,b). The Beta function is a special mathematical function closely related to the Gamma function.

Input Parameters

To calculate, enter positive values for the arguments a and b. Then click the 'Calculate' button.

Properties

Symmetry

The Beta function is symmetric: B(a,b) = B(b,a)

Domain

The parameters a and b must both be positive real numbers.

Applications

Used in probability theory, statistics, and for the Beta distribution.


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