Integral equation of mixed type and integrals of orthogonal polynomials

A method is used to obtain the general solution of the Fredholm–Volterra integral equation of the first kind (FVIEFK) in the space L2(0,a)×C(0,T), 0⩽x⩽a<∞, 0⩽t⩽T<∞. The kernel of the Fredholm integral term is considered in a generalized discontinuous form which belongs to C([0,a]×[0,a]), while the kernel of Volterra integral term is a positive continuous function in the class C(0,T). Many interesting cases of integrals of orthogonal polynomials and spectral relationships are obtained and established from this work.