I posted a four-page set of notes on Chebyshev polynomials on my website 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 *T _{n}*(

*x*) based on his initial in one of the older transliterations.

Good basic summary. Proofs and more are in Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory by Theodore Rivlin (Dover)

Of course, the real spelling is “Чебышёв”, just as it sounds (in Russian.)

Very good explanation. Thanks! Wish I’d seen this about a year ago when I was trying to wrap my head around Чебышёв polynomials for a project in computational methods class.