Quick Python hack-up of one of Ramanujan's pi formulae

ramanuj.py

from mpmath import *

mp.dps = 500
mp.pretty = False

coeff = fdiv(1, fmul(882, sqrt(fadd(fmul(6, sqrt(2)), 1))))

for i in range(0, 5):
    s = 0

    for n in range(0, i):
        a = fac(4 * n) / power(fac(n), 4)
        b = fadd(fsub(106983, fmul(75037, sqrt(2))), fmul(fmul(40, fsub(11133, fmul(7300, sqrt(2)))), n))
        c = fmul(fmul(fmul(power(12, 4 * n), power(fadd(1, sqrt(2)), 20 * n)), power(fadd(1, fmul(2, sqrt(2))), 4 * n)), power(1 + fmul(6, sqrt(2)), fmul(2, n)))

        s = fadd(s, fdiv(fmul(a, b), c))

    result = fmul(coeff, s)

    if abs(result) > 1e-40:
        print(f"{i}:\t{result} => {fdiv(1, result)}")
    else:
        print(f"{i}:\t{result} => nan")