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mo271/.py Secret

Created November 4, 2020 11:27
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.py
In [1]: from mpmath import mp
In [2]: def F(u):
...: return mp.quad(lambda phi: (u*mp.sin(phi)**2)/(mp.sqrt(mp.cos(phi)**2 + u**2*mp.sin(phi)**2)), [0, mp.pi/2])
...: def G(u):
...: return mp.quad(lambda phi: (u*mp.sin(phi)**2)/(mp.sqrt(mp.sin(phi)**2 + u**2*mp.cos(phi)**2)), [0, mp.pi/2])
...: def w(u):
...: return mp.log(F(u)/G(u))
...: def L(u):
...: return F(u)*G(u)
...: def w_prime(u):
...: return mp.diff(w, u)
...: def integrand(u):
...: return L(u)**2*mp.sinh(w(u))*w_prime(u)
...:
In [3]: z = -6*mp.pi**4*mp.quad(integrand, [0,1]); z
Out[3]: mpf('9.1735857548460995')
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