Beta Function Calculator
Beta Function
The Beta function is defined as:
1. Integral Representation:
\( \beta(m, n) = \int_0^1 x^{m-1} (1 - x)^{n-1} \, dx \)
2. Square Root Form:
\( \beta(m, n) = \frac{\sqrt{m} \cdot \sqrt{n}}{\sqrt{m + n}} \)
3. Factorial Form:
\( \beta(m, n) = \frac{(m - 1)! \, (n - 1)!}{(m + n - 1)!} \)
Gamma Function
Gamma of \( n \): \( \Gamma(n) \)
\( \Gamma(n) = \int_0^{\infty} e^{-x} x^{n-1} \, dx \quad (\text{when } n > 0) \)
Recursive Property:
\( \Gamma(n) = n \cdot \Gamma(n-1) = (n - 1)! \)
Step-by-step Instructions
Enter 2 values that can be integers or decimals.
Neither of the numbers can be negative integers or 0.
ß(num1,num2) will be calculated by the program.