The Chebyshev Difference Equation

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