On Gegenbauer polynomials and Wronskian determinants of trigonometric functions
Classical Analysis and ODEs
2025-01-22 v1 Numerical Analysis
Numerical Analysis
Probability
Abstract
M. E. Larsen evaluated the Wronskian determinant of functions . We generalize this result and compute the Wronskian of . We show that this determinant can be expressed in terms of Gegenbauer orthogonal polynomials and we give two proofs of this result: a direct proof using recurrence relations and a less direct (but, possibly, more instructive) proof based on Darboux-Crum transformations.
Keywords
Cite
@article{arxiv.2501.11092,
title = {On Gegenbauer polynomials and Wronskian determinants of trigonometric functions},
author = {Minjian Yuan},
journal= {arXiv preprint arXiv:2501.11092},
year = {2025}
}