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How to prove Chepyshev's polynomials generating function identity?

  1. Dec 21, 2006 #1
    (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. jcsd
  3. Dec 21, 2006 #2
    ?????????????????
     
  4. Dec 21, 2006 #3

    dextercioby

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    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
  5. Dec 21, 2006 #4
    Tn(x)=y
    (1-x^2)y" - xy' + (n^2)y=0
    Am i have to solve this equation?
     
  6. Dec 21, 2006 #5
    i know how to write Chebyshev but it is just a mistake cause of fast typing.
     
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