File:Integergk,k=2,s=0plot.png

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
from mpmath import *
from pylab import rcParams
rcParams['figure.figsize'] = 10, 10

def integerhk(k,t,s):
        return binomial(t-s,k)
def integergk(k,t,s):
        return ((-1)**k)*integerhk(k,s,t)
def g(x):
        return 0

x=np.arange(-10,10,1)
x2=np.arange(-20,20,1)
f=np.vectorize(lambda x: integergk(2,x,0))
y=f(x)
h=np.vectorize(g)
y2=h(x2)

fig, ax = plt.subplots()

plt.xlabel(r'$t$')
plt.ylabel(r'$g_2(t,0;\mathbb{Z})$')
plt.title(r'Time scale $g_k$ monomial function')

xlabels = [item.get_text() for item in ax.get_yticklabels()]
xlabels=[r'$-10$',r'$-5$',r'$-1$',r'$0$',r'$5$',r'$10$',r'$15$']
ax.set_xticks([-10,-5,-1,0,5,10,15])
ax.set_xticklabels(xlabels)

plt.scatter(x,y,color='Black',s=40)
plt.plot(x2,y2,':',linewidth=2,color='Black')

plt.xlim([-10.3,10.3])

plt.savefig('integergk,k=2,s=0plot.png',bbox_inches='tight',pad_inches=0.15)