On the method of solution for a kind of nonlinear singular integral equation (Q705411)

The author considers the nonlinear singular integral equation \[ \phi(t)^{2}+\frac{2b}{\pi i}\int_{L}\frac{\phi(\tau)}{\tau-t}d\tau=f(t), \quad t\in L, \] where \(L\) is a closed countour in the complex plane, \(b\not=0\) is a constant and \(f(t)\) is a polynomial. Certain special cases of the above equation are considered.