import numpy as np
 
#なんたらのアルゴリズム。いっぱい繰り返す
def GaussRegendre(N):
    #初項
    a = 1.0
    b = np.sqrt(2) / 2
    t = 1 / 4
    p = 1
 
    for i in range(N): #←コレ、iが0からN-1までの間以下を繰り返すらしいですよ？
 
        #漸化式（？）に従い、次の項を計算
        a_new = (a + b) / 2
        b_new = np.sqrt(a * b)
        t_new = t - p * (a - a_new)**2
        p_new = 2 * p
 
        #古い値を新しい値に置き換え
        a = a_new
        b = b_new
        t = t_new
        p = p_new
 
    pi = (a + b)**2 / (4 * t) #円周率の計算（ここすき）
    return pi
 
#出力
print("GaussRegendre(1) = " + str(GaussRegendre(1)))
print("GaussRegendre(2) = " + str(GaussRegendre(2)))
print("GaussRegendre(3) = " + str(GaussRegendre(3)))

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