Chebyshev Polynomials

doi:10.1117/3.2207310.ch06

Book: Special Functions for Optical Science and Engineering

Author(s): Vasudevan Lakshminarayanan, L. Srinivasa Varadharajan

Published: 2015

https://doi.org/10.1117/3.2207310.ch06

Author Affiliations +

Abstract

The first thing to note about Chebyshev polynomials is that the mathematician’s name is transliterated in various forms: Tchebychef, Tchebycheff, Tschebyscheff, Chebysheff, etc. These iterations all identify the same Russian mathematician, Pafnuty Lvovich Chebyshev (1821–1894). These polynomials arise as the solutions of differential equations. The corresponding solutions are denoted as Tn(x) and Un(x) and are known as Chebyshev polynomials of the first and second kind, respectively. These polynomials are related to trigonometric multi-angle formulas.