Basel_Problem_Euler.py

# https://en.wikipedia.org/wiki/Basel_problem
# Leonhard Euler solved it in 1734
# and published it in 1735 St Peterburg's Adacemy of Sciences
# Basel problem is Riemann's zeta-function at value s = 2
# https://en.wikipedia.org/wiki/Riemann_zeta_function

# Juhani Kaukoranta 23.6.2018

import math
import numpy as np


def Basel():
    '''reciprocals, 1/n'''
    a = np.reciprocal(np.arange(1,500000000,1.0))
    '''sum of 1/(n*n)'''
    summa = np.sum(np.multiply(a,a))
    return(summa)

print(" Basel problem sum = ",Basel())
print("Pii^2 / 6 = ",math.pi*math.pi/6)