"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | + | ==introduction</h5> | |
* borrowed from [[Andrews-Gordon identity]] | * borrowed from [[Andrews-Gordon identity]] | ||
| 13번째 줄: | 13번째 줄: | ||
| − | + | ==diagonals of polygon</h5> | |
Clear[r]<br> r[i_] := Sin[((i + 1) Pi)/7]/Sin[Pi/7]<br> Table[N[r[i], 10], {i, 0, 5}]<br> Table[N[r[i]^2 - (1 + r[i - 1] r[i + 1]), 10], {i, 1, 4}] | Clear[r]<br> r[i_] := Sin[((i + 1) Pi)/7]/Sin[Pi/7]<br> Table[N[r[i], 10], {i, 0, 5}]<br> Table[N[r[i]^2 - (1 + r[i - 1] r[i + 1]), 10], {i, 1, 4}] | ||
| 21번째 줄: | 21번째 줄: | ||
| − | + | ==chebyshev polynomials</h5> | |
* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식] | * [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식] | ||
| 30번째 줄: | 30번째 줄: | ||
| − | + | ==history</h5> | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 38번째 줄: | 38번째 줄: | ||
| − | + | ==related items</h5> | |
* [[sl(2) - orthogonal polynomials and Lie theory]] | * [[sl(2) - orthogonal polynomials and Lie theory]] | ||
| 56번째 줄: | 56번째 줄: | ||
| − | + | ==books</h5> | |
| 87번째 줄: | 87번째 줄: | ||
| − | + | ==question and answers(Math Overflow)</h5> | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
| 96번째 줄: | 96번째 줄: | ||
| − | + | ==blogs</h5> | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 106번째 줄: | 106번째 줄: | ||
| − | + | ==experts on the field</h5> | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
| 114번째 줄: | 114번째 줄: | ||
| − | + | ==links</h5> | |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
* [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내] | * [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내] | ||
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | ||
2012년 10월 28일 (일) 12:56 판
==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 \(d_0=1\), \(d_k=1\)
- (*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}]
==diagonals of polygon
Clear[r]
r[i_] := Sin[((i + 1) Pi)/7]/Sin[Pi/7]
Table[N[r[i], 10], {i, 0, 5}]
Table[N[r[i]^2 - (1 + r[i - 1] r[i + 1]), 10], {i, 1, 4}]
==chebyshev polynomials
- 체비셰프 다항식
- http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html
also obey the interesting determinant identity
==history
==related items
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
==books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
- 논문정 리
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
==question and answers(Math Overflow)
==blogs
==experts on the field
==links