The gamma function

The gamma function is related to the factorial by $\Gamma(x) = (x-1)!$ and both are plotted in the code below. Note that $\Gamma(x)$ is not defined for negative integer $x$, which leads to discontinuities in the plot.

import numpy as np
from scipy.special import gamma
import pylab

# The Gamma function
ax = pylab.linspace(-5, 5, 1000)
pylab.plot(ax, gamma(ax), ls='-', c='k', label='$\Gamma(x)$')

# (x-1)! for x = 1, 2, ..., 6
ax2 = pylab.linspace(1,6,6)
xm1fac = np.array([1, 1, 2, 6, 24, 120])
pylab.plot(ax2, xm1fac, marker='*', markersize=12, markeredgecolor='r',
           markerfacecolor='r', ls='',c='r', label='$(x-1)!$')

pylab.xlim(-5, 5)

The gamma and factorial functions