6 papers
Old structures, a vanishing formula
K. Castillo, G. Gordillo-Núñez
We identify a normalization defect in a determinantal construction of fourth-order Hahn difference equations and compare its scalar equation with Foupouagnigni's 1998 elimination a…
The manufacture of examples II: the "para-classical" orthogonal polynomials
K. Castillo, G. Gordillo-Núñez
Under the stated regularity assumptions, the full orthogonality functionals of the five finite para-families considered here are classical for the respective affine, quadratic, …
Yet Another Characterisation of Classical Orthogonal Polynomials?
K. Castillo, G. Gordillo-Núñez
The NIST Handbook of Mathematical Functions (2010) and the NIST Digital Library of Mathematical Functions (2025) classify classical orthogonal polynomials through Bochner's 1929 al…
Wendroff's theorem beyond consecutive degrees and related inverse spectral problems
K. Castillo, G. Gordillo-Núñez
A classical theorem of Wendroff shows that one may reconstructs a sequence of orthogonal polynomials on the real line from two non-constant polynomials of consecutive degrees whose…
The Nikiforov-Uvarov method
Guillermo Gordillo-Núñez
We review the so-called Nikiforov-Uvarov method along with some basic results about classical orthogonal polynomials and hypergeometric functions related to the hypergeometric diff…
The Schrödinger equation for the Rosen-Morse type potential revisited with applications
Guillermo Gordillo-Núñez, Renato Alvarez-Nodarse, Niurka R. Quintero
We rigorously solve the time-independent Schrödinger equation for the Rosen-Morse type potential. By using the Nikiforov-Uvarov method, we obtain, in a systematic way, the complete…