  We evaluate the density of states (DOS) associated with tridiagonal symmetric
Hamiltonian matrices and study the effect of perturbation on one of its
entries. Analysis is carried out by studying the resulting three-term recursion
relation and the corresponding orthogonal polynomials of the first and second
kind. We found closed form expressions for the new DOS in terms of the original
one when perturbation affects a single diagonal or off-diagonal site or a
combination of both. The projected DOS is also calculated numerically and its
relation to the average DOS is explored both analytically and numerically.
