"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 20개는 보이지 않습니다) | |||
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| − | + | ==introduction== | |
* borrowed from [[Andrews-Gordon identity]] | * borrowed from [[Andrews-Gordon identity]] | ||
| − | * quantum dimension and thier recurrence relation | + | * 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> | ||
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| − | + | ==diagonals of regular polygon== | |
| − | + | * length of hepagon | |
| + | :<math>d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} </math> | ||
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| − | + | ==chebyshev polynomials== | |
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* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식] | * [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식] | ||
| − | * http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html | + | * http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity |
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| − | + | ==related items== | |
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* [[sl(2) - orthogonal polynomials and Lie theory]] | * [[sl(2) - orthogonal polynomials and Lie theory]] | ||
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| − | + | ==articles== | |
| − | * [http://www.jstor.org/stable/2691048 Golden Fields: A Case for the Heptagon] | + | * [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 | ** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31 | ||
| − | + | [[분류:개인노트]] | |
| − | + | [[Category:quantum dimensions]] | |
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2020년 12월 28일 (월) 04:01 기준 최신판
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 \(d_0=1\), \(d_k=1\)
diagonals of regular polygon
- length of hepagon
\[d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} \]
chebyshev polynomials
- 체비셰프 다항식
- http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting determinant identity
articles
- Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31