"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이

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74번째 줄: 74번째 줄:
 
** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
 
** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
  
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* [[2010년 books and articles|논문정 리]]
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* http://www.ams.org/mathscinet
 
* http://www.ams.org/mathscinet
 
* http://www.zentralblatt-math.org/zmath/en/
 
* http://www.zentralblatt-math.org/zmath/en/

2012년 11월 3일 (토) 03:01 판

introduction

  • borrowed from Andrews-Gordon identity
  • quantum dimension and thier 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}]

 

 

diagonals of polygon

Clear[r]
r[i_] := Sin[((i + 1) Pi)/7]/Sin[Pi/7]
Table[N[r[i], 10], {i, 0, 5}]
Table[N[r[i]^2 - (1 + r[i - 1] r[i + 1]), 10], {i, 1, 4}]

 

 

chebyshev polynomials

 

 

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