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

2010년 11월 26일 (금) 08:43 판

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 \(d_0=1\), \(d_k=1\)

(*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
Plot[d[k, i], {i, 0, 2 k}]

Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31

@@ 2번째 줄: / 2번째 줄: @@
 * borrowed from [[Andrews-Gordon identity]]
-*  quantum dimension and there recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
+*  quantum dimension and thier recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
@@ 31번째 줄: / 31번째 줄: @@
 <h5>related items</h5>
+* [[sl(2) - orthogonal polynomials and Lie theory]]