Residue of psi*w at x0 (times w(x0)^-1): -(2*m**4*mu*sigma**2 - 2*m**4*mu*sigma - m**4*sigma**3 - m**4*sigma**2 - 2*m**2*mu*sigma**2 + 2*m**2*mu + 4*m**2*sigma**2 + m**2*sigma - m**2 + 2*mu*sigma - 2*mu - 4*sigma + 2)/(2*m**2*sigma*(sigma - 1)*(m**2*sigma - 1))
mu* (own, from the series) = (m**2*sigma + m**2 - 2)*(m**2*sigma**2 - 2*sigma + 1)/(2*(m - 1)*(m + 1)*(sigma - 1)*(m**2*sigma - 1))
mu* (claim)                 = (m**2*sigma + m**2 - 2)*(m**2*sigma**2 - 2*sigma + 1)/(2*(m - 1)*(m + 1)*(sigma - 1)*(m**2*sigma - 1))
equal: True
kappa - R simplifies to: 0
a^2 - b^2 - (a''^2 - b''^2) = 0
a''^2 = a^2 - lambda: True ; b''^2 = b^2 - lambda: True
(sn*cn)^2 - x(1-x) with x = sn^2, cn^2 = 1 - sn^2: 0
kappa_4 = 2 ; kappa_6 = -(a - 2*b)*(a + b)**2/(b**2*(2*a + b)) ; claim kappa_6 = (a+b)^2(2b-a)/(b^2(2a+b)): True
kappa_6 * A'A (N=6, A'A = 4a^2b^2(2a+b)(a+2b)/(a+b)^2) = -4*a**2*(a - 2*b)*(a + 2*b)
kappa_4 * A'A (N=4, A'A = 8a^2b^2) = 16*a**2*b**2
x0 - 1 =  -(m**2*sigma - 1)/(m**2*sigma)  (> 0 since m^2 sigma < 1)
