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 L-2(0, a) x C(0, T), 0 less than or equal to x less than or equal to a < infinity, 0 less than or equal to t less than or equal to T < infinity. The kernel of the Fredholm integral term is considered in a generalized discontinuous form which belongs to C([0, a] x [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. (C) 2002 Elsevier Science B.V. All rights reserved.