I posted a four-page set of notes on Chebyshev polynomials on my web site this morning. These polynomials have many elegant properties that are simple to prove. They’re also useful in applications.
Mr. Chebyshev may have the honor of the most variant spellings for a mathematician’s name. I believe “Chebyshev” is now standard, but his name has been transliterated from the Russian as Chebychev, Chebyshov, Tchebycheff, Tschebyscheff, etc. His polynomials are denoted Tn(x) based on his initial in one of the older transliterations.