Abstract
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)×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.