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

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imported>Pythagoras0
imported>Pythagoras0
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==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
 
$$d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} $$
 
 
 
 
 
==chebyshev polynomials==
 
 
* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식]
 
* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html<br> also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity
 
 
 
 
 
 
 
 
==history==
 
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
 
 
 
 
 
 
 
==related items==
 
 
* [[sl(2) - orthogonal polynomials and Lie theory]]
 
 
 
 
 
 
 
 
==articles==
 
 
* [http://www.jstor.org/stable/2691048 Golden Fields: A Case for the Heptagon]<br>
 
** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
 
 
[[분류:개인노트]]
 
[[Category:quantum dimensions]]
 

2020년 11월 12일 (목) 19:47 판