RiemannZeta4_rapid.py

# Calculates Riemann's Zeta(4)
# using rapid algorithm
# Juhani Kaukoranta 24.6.2018

from decimal import *
import math
import time


def Binomial(n,k):
    a = math.factorial(n)//(math.factorial(n-k)*math.factorial(k))
    return(a)

def Zeta4(precision):
    getcontext().prec=precision
    r = Decimal(0)
    for n in range(1,2*precision):
        r = r + Decimal(1)/(n*n*n*n*Binomial(2*n,n))
    return(36*r/17)

precision = int(input("How many numbers precision, f.eq 100 "))
time0 = time.clock()
print("Apery constant , Zeta(4) = ",Zeta4(precision))
print("Pi^4/90 = ",math.pi**4/90)
time1 = time.clock()
print("calculation time ",time1-time0," seconds")