"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 6번째 줄: | 6번째 줄: | ||
:<math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math> | :<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== | ==diagonals of regular polygon== | ||
| 12번째 줄: | 12번째 줄: | ||
:<math>d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} </math> | :<math>d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} </math> | ||
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==chebyshev polynomials== | ==chebyshev polynomials== | ||
| 19번째 줄: | 19번째 줄: | ||
* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity | * http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity | ||
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==related items== | ==related items== | ||
| 27번째 줄: | 27번째 줄: | ||
* [[sl(2) - orthogonal polynomials and Lie theory]] | * [[sl(2) - orthogonal polynomials and Lie theory]] | ||
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==articles== | ==articles== | ||
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