# Gamma Function Calculator

 An easy to use calculator to compute Gamma function $$\Gamma \; (z)$$ defined by the integral $\displaystyle \Gamma (z) = \int_0^{\infty} \; t^{z-1}e^{-t} \; dt$ is presented.
The graph of the error function $$\Gamma (x)$$, for real $$x$$, is shown below as well as its reciprocal $$\dfrac{1}{\Gamma (x)}$$ . ## Properties of Gamma Function

It can be shown that for positive integers $\Gamma(n) = (n - 1)!$ hence
$$\quad \Gamma(1) = (1 - 1)! = 0! = 1$$
$$\quad \Gamma(2) = (2 - 1)! = 1! = 1$$
$$\quad \Gamma(3) = (3 - 1)! = 2! = 2$$
$$\quad \Gamma(4) = (4 - 1)! = 3! = 6$$
valeus that can be checked in the graph above.

The Gamma function $$\Gamma(z)$$ is used to extend the factorial function to complex numbers.

Using imptoper integrals and integration by parts, it can be shown that $\Gamma(z+1) = z \Gamma(z)$ for $$z$$ in the complex plane sucth that $$\Re (z) \gt 0$$

## Use Calculator

Enter the the real and imagianry parts $$Re \; z$$ and $$Im \; z$$ respectively of the argument $$z$$ of the Gamma function, and the number of decimal places desired, then click "Calculate".

 $$\quad Re \; z =$$ 2.1 $$\quad Im \; z =$$ 0.5 Decimal Places Desired = 8