Abstract

This study is focused on the development of a new generalized version of four known types of Chebyshev polynomials. We come up with four different kind of generalized Chebyshev polynomials using a modified recurrence relationship with different starting points. We also get Binet's formula for generalized Chebyshev’s polynomials. The Binet formula is obtained by mathematical induction. The matrix representation and the characteristic equation are presented using matrix algebra properties for these polynomials. We also explore about the sum, products, and subtraction of the roots of the characteristic equation of the generalized Chebyshev polynomials. Finally, we have shown how Chebyshev-like polynomials can be used in practice with examples.

Keywords and Phrases

Generalized Chebyshev polynomials, Recurrences Relation, Binet-Like Formula, Matrix Representation, Characteristic Equations.

A.M.S. subject classification

11C08, 11B37, 11B39.

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