Year: 2014
Type: preprint
Abstract: A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of Bessel functions. The measure of orthogonality for this new class is described explicitly. In addition, the orthogonality measure problem is also discussed on a more general level. Apart of this, various identities derived for the new orthogonal polynomials may be viewed as generalizations of some formulas known from the theory of Bessel functions. A key role in these derivations is played by a Jacobi (tridiagonal) matrix $J_{L}$ whose eigenvalues coincide with reciprocal values of the zeros of the regular Coulomb wave function $F_{L}(η,ρ)$. The spectral zeta function corresponding to the regular Coulomb wave function or, more precisely, to the respective tridiagonal matrix is studied as well.
Source: arXiv (Cornell University)
Authors: Stampach, Frantisek, Stovicek, Pavel
Institution: Czech Technical University in Prague
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952040928