Cyclotomic numbers and Chebyshev polynomials

수학노트
http://bomber0.myid.net/ (토론)님의 2010년 11월 22일 (월) 20:13 판
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introduction
  • borrowed from Andrews-Gordon identity
  • quantum dimension and there recurrence relation
    \(d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}\) satisfies
    \(d_i^2=1+d_{i-1}d_{i+1}\) where \(d_0=1\), \(d_k=1\)

 

  1. (*choose k for c (2,k+2) minimal model*)k := 11
    d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]
    Table[{i, d[k, i]}, {i, 1, k}] // TableForm
    Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,
       k}] // TableForm
  2. Plot[d[k, i], {i, 0, 2 k}]

 

 

chebyshev polynomials

 

 

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