Gamma Function Calculator

Gamma Function Calculator

Calculate the Gamma function using the formula:
\[ \Gamma(z) = \int_0^\infty t^{z-1} e^{-t}\, dt = \frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \quad (\text{for related Beta functions}) \]
(Here, we use the Lanczos approximation for \(\Gamma(z)\).)

* Enter a positive value for \( z \).

Step 1: Enter Parameter

Example: 2.5

Gamma Function Formula (via Lanczos approximation):
\(\Gamma(z) = \sqrt{2\pi}\,t^{z+\frac{1}{2}}e^{-t}\, x\), where \(t=z+g+0.5\) and \(x=0.99999999999980993+\sum_{i=0}^{n-1}\frac{p_i}{z+i+1}\).


Practical Example:
For \(z = 2.5\), the Gamma function is computed to be approximately \( \Gamma(2.5) \approx 1.32934 \).