Gamma Function

This function calculates Euler's gamma function. The gamma function is one of the most important special functions and is used in analysis and function theory. It is denoted by the Greek capital letter Γ (gamma).

To perform the calculation, enter the argument x. Then click the calculate button.

To read the individual values move the mouse over the graphic.

If x is an integer, the result is ±∞. In order to better display small values, the Y-scale is limited to +/- 20.

Formula for Euler's gamma function

\(\displaystyle \Gamma(x)=\int_0^∞t^{x-1}e^{-t}dt, \)   wenn \(\displaystyle Re(x) >0 \)

\(\displaystyle \Gamma(a)= \frac{\Gamma(a+1) }{a},\)   \(\displaystyle \Gamma(a)\Gamma(1-a)=\frac{\pi}{sin(\pi a)} \)

\(\displaystyle \Gamma(n+1)=n!,\)   \(\displaystyle \Gamma\left( \frac{1}{2} \right) = \sqrt{\pi} \)

A detailed description can be found at Wikipedia