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Open AccessFeature PaperArticle

The Chebyshev Difference Equation

1
Department of Computer Science and Math, Fairmont State University, Fairmont, WV 26554, USA
2
TMC2 Technologies of West Virginia, Fairmont, WV 26554, USA
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 74; https://doi.org/10.3390/math8010074
Received: 22 December 2019 / Revised: 30 December 2019 / Accepted: 31 December 2019 / Published: 3 January 2020
(This article belongs to the Special Issue Special Functions and Applications)
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. View Full-Text
Keywords: discrete analogue; special function; Chebyshev polynomial; difference equation; generalized hypergeometric series discrete analogue; special function; Chebyshev polynomial; difference equation; generalized hypergeometric series
MDPI and ACS Style

Cuchta, T.; Pavelites, M.; Tinney, R. The Chebyshev Difference Equation. Mathematics 2020, 8, 74.

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