Math Is Fun Forum

zetafunc.

Guest

nth chebyshev polynomials (of first kind, second kind, etc.)

can someone explain what these are?

what is the nth chebyshev polynomial of the first kind, for example?

thanks^^

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: nth chebyshev polynomials (of first kind, second kind, etc.)

Hi zetafunc.;

You are asking a lot questions of this type and that is both good and bad. Do you have some firm basis for understanding the answers? Is your question rooted in some problem that you are working on? Otherwise it may just serve to confuse you.

Here is one answer, they are the solutions to certain DE's and because they are orthogonal  along with the Legendre polynomials they are a superior basis for curve fitting and the economization of functions than are the standard powers of x (Taylor Series). In other words they have the highly desirable min-max property. This part is well covered in numerical analysis.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.