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MathGroup Archive 2004

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Chebyshev's Identity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46494] Chebyshev's Identity
  • From: "Ravinder Kumar B." <ravi at crest.ernet.in>
  • Date: Fri, 20 Feb 2004 06:53:42 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Friends,
I have a (2x2) matrix raised to power n.

M = ({{Cos[x/n]*Exp[-iy/n],
Sin[x/n]*Exp[-iy/n]},{-Sin[x/n]*Exp[iy/n],Cos[x/n]*Exp[iy/n]}})^n;

All I know at present is that this expression can be further
simplified analytically using Chebyshev's identity to much a simpler
expression in the limit n -> infinity.
I am unable to find any information regarding Chebyseb's identity and its
usage.
Could some one please tell me more about this identity and its usage in
solving above expression. Mathematica fails to do it analytically.

-- 
    Regards,                                   Feb 20
    ravi


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