Comments on: An ODE, Orthogonal Functions, and the Chebyshev Polynomials http://artent.net/2013/09/16/an-ode-orthogonal-functions-and-the-chebyshev-polynomials/ We're blogging machines! Wed, 15 Jan 2025 16:08:06 +0000 hourly 1 http://wordpress.org/?v=4.0 By: hundalhh http://artent.net/2013/09/16/an-ode-orthogonal-functions-and-the-chebyshev-polynomials/#comment-1904 Wed, 25 Sep 2013 18:43:27 +0000 http://162.243.213.31/?p=2098#comment-1904 I wonder if there is some way to know ahead of time or intuit that the result is going to be polynomial.

I guess for any weight function, it’s possible to get orthogonal polynomials, but the Chebyshev polynomials are so nice—integer coefficients and all.

]]> By: Leo http://artent.net/2013/09/16/an-ode-orthogonal-functions-and-the-chebyshev-polynomials/#comment-1899 Wed, 25 Sep 2013 15:09:18 +0000 http://162.243.213.31/?p=2098#comment-1899 Hum..
seems that Mr Tchebychev followed the same thinking path..

]]> By: ThePig http://artent.net/2013/09/16/an-ode-orthogonal-functions-and-the-chebyshev-polynomials/#comment-1879 Sat, 21 Sep 2013 16:18:59 +0000 http://162.243.213.31/?p=2098#comment-1879 This post reminds me of a friend who used to chastise me when I used “orthogonal” when I meant “independent.” For sin x and cos x are orthogonal but they are clearly not independent.

]]>