The Chebyshev Difference Equation

Tom Cuchta, Michael Pavelites and Randi Tinney
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Tom Cuchta: Department of Computer Science and Math, Fairmont State University, Fairmont, WV 26554, USA
Michael Pavelites: Department of Computer Science and Math, Fairmont State University, Fairmont, WV 26554, USA
Randi Tinney: TMC 2 Technologies of West Virginia, Fairmont, WV 26554, USA

Mathematics, 2020, vol. 8, issue 1, 1-11

Abstract: We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind. The resulting “discrete Chebyshev polynomials” of the first and second kind have qualitatively similar properties to their continuous counterparts, including a representation by hypergeometric series, recurrence relations, and derivative relations.

Keywords: discrete analogue; special function; Chebyshev polynomial; difference equation; generalized hypergeometric series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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