Beta Function Calculator

Beta Function Calculator calculator can be used to compute the Beta function \( \text{Beta}(x, y) \) for given values of \( x \) and \( y \). The Beta function is an important special function in mathematics used in probability theory, statistics, and other fields.

Input Parameters

Calculation Results

Calculation Formula

The Beta function is calculated as:

\[ \text{Beta}(x, y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)} \]

Where:
\( \Gamma(z) \) is the Gamma function.

Beta Function Calculator Calculator Usage Guide

Learn how to use the Beta Function Calculator calculator and its working principles

How to Use the Calculator

  1. Enter the value of parameter \( x \) in the first input field. This value must be greater than 0.
  2. Enter the value of parameter \( y \) in the second input field. This value must also be greater than 0.
  3. Click the "Calculate" button to compute the Beta function \( \text{Beta}(x, y) \).
  4. The result will be displayed in the result field.

Understanding the Beta Function

The Beta function \( \text{Beta}(x, y) \) is a special function that is related to the Gamma function. It is defined as the integral of \( t^{x-1} (1-t)^{y-1} \) from 0 to 1. The Beta function is used in various areas of mathematics and statistics, including probability theory, combinatorics, and the calculation of certain integrals.

Formula

The Beta function can be computed using the Gamma function as follows:

\[ \text{Beta}(x, y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)} \]

Example

If you enter \( x = 2 \) and \( y = 3 \), the calculator will compute \( \text{Beta}(2, 3) \) as follows:

\[ \text{Beta}(2, 3) = \frac{\Gamma(2) \Gamma(3)}{\Gamma(5)} = \frac{1! \cdot 2!}{4!} = \frac{1 \cdot 2}{24} = \frac{2}{24} = \frac{1}{12} \approx 0.08333 \]