Combinatorially Composing Chebyshev Polynomials

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Daniel Walton '07, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

8-2010

Abstract

We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n ≥ 0, T_m(T_n(x)) = T_mn(x) and U_m-1 (T_n(x))U_n-1(x) = U_mn-1(x).

Comments

First published in Journal of Statistical Planning and Inference, Proceedings of the 6th International Conference on Lattice Path Combinatorics, Vol. 140, Issue 8, pp. 2161-2167, 2010.

This article is also available at http://www.sciencedirect.com/science/article/pii/S0378375810000236.

Rights Information

© 2010 Elsevier B.V.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.jspi.2010.01.012

Recommended Citation

Benjamin, A.T., & Walton, D. (2010). Combinatorially composing Chebyshev polynomials. Journal of Statistical Planning and Inference, 140(8): 2161-2167. DOI: 10.1016/j.jspi.2010.01.012