Função Beta B(x,y)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The beta function B(x,y) is a special function defined as B(x,y) = Γ(x)Γ(y)/Γ(x+y), where Γ represents the gamma function. This calculator computes the beta function for positive real numbers x and y. The beta function is widely used in statistics, probability, and mathematical analysis, particularly in beta distributions and integral calculations.
To use the calculator, simply input the values of x and y. The calculation relies on the gamma function relation, which generalizes factorials to complex numbers. The beta function is symmetric, meaning B(x,y) = B(y,x). It also has applications in probability theory, where it's linked to the beta distribution, used to model random variables between 0 and 1.
Note that the gamma function Γ(n) is undefined for non-positive integers. Thus, x and y must be positive real numbers. For very large or near-zero values, computational limitations may arise. The calculator uses numerical algorithms for accurate approximations, but results may vary slightly depending on implementation.
Frequently asked questions
What is the beta function used for?
The beta function is used in statistics for beta distributions, probability calculations, and definite integrals. It also appears in probability theory and variable transformations.
How does the calculator compute the beta function?
The calculator uses the relation B(x,y) = Γ(x)Γ(y)/Γ(x+y). For complex values, it implements numerical algorithms approximating the gamma function and performing division.
Can I use negative numbers or zero?
No. The gamma function is undefined for non-positive integers, and the beta function requires positive x and y to avoid division by zero or undefined values.
Why is the beta function symmetric?
It's symmetric because Γ(x)Γ(y) is commutative and Γ(x+y) equals Γ(y+x). Therefore, B(x,y) = B(y,x) is always true.
What precautions should I take with very large values?
Extremely large values may cause numerical overflow. It's recommended to use scientific notation or scale down inputs to prevent calculation errors.