An analytical solution for the overlap determinant det Sn

This chapter deals with an analytical solution for the overlap determinant det S_n. It presents a finding which exhibits a remarkably regular factorability of the general result for H_n(c₀) as a direct consequence of a judicious combination of symmetry of the Hankel determinant and the Lanczos orthogonal polynomials. Thus, given either the set {β_v} or {q_v,0}, the Hankel determinant H_n (c₀), or equivalently, the overlap determinant det S_n in the Schrödinger, i.e. Krylov basis {| φ_n)} can be constructed.