Some results on the dual series equations (Q1061972)

The author considers the dual series equations with general kernels of the form: \(\sum^{\infty}_{n=0}A_ n\gamma (n)\psi_ n(x)=f_ k(x)\), \(\sum^{\infty}_{n=0}A_ n\psi_ n(x)=0\) where the coefficients \(A_ n\) are to be determined. Using generalized integral transformations the above set is reduced to an equivalent system of integral equations, which is then solved by the method of successive approximations.