[Kelvin Wedge] Fourier Coefficients of Quadratic Forms in $\cos \gamma$ for Steady Capillary-Gravity Waves
The math is sound. The method is not. We factor the quadratic denominator \(a+b \cos \gamma+c \cos ^2 \gamma\) and reduce the computation of its Fourier coefficients to those of \(1 /(\cos \gamma-\lambda)\). Solving the associated second-order recurrence for the Fourier coefficients yields a closed-form expression in terms of \(\lambda_{ \pm}\)and \(q_{ \pm}=\lambda_{ \pm}+i \sqrt{1-\lambda_{ \pm}^2}\), leading to the final explicit formula for \(c_m(k)\) in the steady ship-wave setting.