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

2020년 12월 28일 (월) 04:01 기준 최신판

\[d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}\] satisfies \[d_i^2=1+d_{i-1}d_{i+1}\] where \(d_0=1\), \(d_k=1\)

\[d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} \]

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

@@ 1번째 줄: / 1번째 줄: @@
+==introduction==
+* borrowed from [[Andrews-Gordon identity]]
+*  quantum dimension and thier recurrence relation
+:<math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}</math> satisfies
+:<math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math>
+==diagonals of regular polygon==
+* length of hepagon
+:<math>d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} </math>
+==chebyshev polynomials==
+* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식]
+* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity
+==related items==
+* [[sl(2) - orthogonal polynomials and Lie theory]]
+==articles==
+* [http://www.jstor.org/stable/2691048 Golden Fields: A Case for the Heptagon]
+** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
+[[분류:개인노트]]
+[[Category:quantum dimensions]]