shit.py

import matplotlib.pyplot as plt
import numpy as np


def p(t, alpha=1.0, beta=1.0, p0=1.0):
    return beta ** t * p0 + sum([alpha * beta ** (t - m) for m in range(1, t + 1)])


vec_p = np.vectorize(p)
times = np.arange(10)
alphas = np.arange(-5, 5, 0.1)
output = []

for t in times:
    output.append(vec_p(t, alphas, beta=5))

plt.plot(times, output)
plt.show()