On Gegenbauer polynomials and Wronskian determinants of trigonometric functions
Abstract
M. E. Larsen evaluated the Wronskian determinant of functions \(mx)\1 m n. We generalize this result and compute the Wronskian of \(mx)\1 m n-1 \((k+n)x\ . 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.
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