Homework Help: How to prove Chepyshev's polynomials generating function identity?

1. Dec 21, 2006

aligator123

(1-xt)/(1-2xt+t^2)=sum(Tn(x)t^n)
How can i prove this equation?

Could you give me a hint or suggestion?

2. Dec 21, 2006

aligator123

?????????????????

3. Dec 21, 2006

dextercioby

What's the definition of Chebyshev's polynomials ? I'd also hint that you can use the ODE which the polynomials solve exactly.

Daniel.

P.S. The "p" in "Chepyshev" is actually reversed upside down and it's a "b".

Last edited: Dec 21, 2006
4. Dec 21, 2006

aligator123

Tn(x)=y
(1-x^2)y" - xy' + (n^2)y=0
Am i have to solve this equation?

5. Dec 21, 2006

aligator123

i know how to write Chebyshev but it is just a mistake cause of fast typing.