# ガウス＝ルジャンドルのアルゴリズム
a0 = 1.0
b0 = 0.5**0.5
c0 = 0.5
p0 = 1.0
 
def A(n):
    if n==0:
        return a0
    else:
        return (A(n-1) + B(n-1)) / 2
 
def B(n):
    if n==0:
        return b0
    else:
        return (A(n-1) * B(n-1))**0.5
 
def C2(n):
    if n==0:
        return c0
    else:
        return A(n)**2 - B(n)**2
 
def S(n):
    res = 0
    for j in range(1,n+1):
        res += 2**j * C2(j)
    return res
 
N = 3
pi = (A(N) + B(N))**2 / (1 - 2*S(N))
print(pi)
 

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