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The Fair-Luke algorithm, as appears in Rational Approximations to the Solution of the Second Order Riccati Equation, constructs rational functions which approximate solutions of the so-called “generalized second order Riccati equation” $ $ (A_0+B_0y)y”+(C_0+D_0y)y’-2B_0(y’)^2+E_0+F_0 y+G_0 y^2+H_0y^3=0 \tag{1}$ $ where the coefficients have the form $ $ \begin{align} &A_0=x^2 \sum a_k x^k, \quad B_0=x^2 \sum b_kRead more