Cyclotomic numbers and Chebyshev polynomials - 편집 역사

2020년 12월 28일 (월) 12:01에 Pythagoras0님의 편집

2020-12-28T12:01:17Z

2020-11-16T12:25:32Z

2020-11-16T10:56:00Z

2020-11-16T10:30:19Z

2020-11-13T03:51:28Z

Undo imported revision 33826 by user imported>Pythagoras0

2020-11-13T03:47:02Z

2020-11-13T03:47:02Z

2017-11-19T11:58:32Z

2013-12-01T21:44:57Z

articles

2013-08-05T12:31:26Z

@@ 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>
-−
 ==diagonals of regular polygon==
@@ 12번째 줄: / 12번째 줄: @@
 :<math>d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} </math>
-−
 ==chebyshev polynomials==
@@ 19번째 줄: / 19번째 줄: @@
 * http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity
-−
-−
 ==related items==
@@ 27번째 줄: / 27번째 줄: @@
 * [[sl(2) - orthogonal polynomials and Lie theory]]
-−
-−
 ==articles==

@@ 10번째 줄: / 10번째 줄: @@
 ==diagonals of regular polygon==
 * length of hepagon
-$$d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} $$
+:<math>d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} </math>

← 이전 판		2020년 11월 16일 (월) 10:56 판
18번째 줄:		18번째 줄:
	* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식]		* [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		* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity
−
−
−
−
−
−	~~==history==~~
−
−	* http://www.google.com/search?hl=en&tbs=tl:1&q=

@@ 17번째 줄: / 17번째 줄: @@
 * [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
+* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity
@@ 41번째 줄: / 41번째 줄: @@
 ==articles==
-* [http://www.jstor.org/stable/2691048 Golden Fields: A Case for the Heptagon]<br>
+* [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]]

← 이전 판	2020년 11월 13일 (금) 03:51 판
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
	+	$$d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} $$
	+
	+
	+
	+	==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]]

← 이전 판	2020년 11월 13일 (금) 03:47 판
(차이 없음)

@@ 4번째 줄: / 4번째 줄: @@
 *  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><br>
+:<math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math>
-#  (*choose k for c (2,k+2) minimal model*)k := 11<br> d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]<br> Table[{i, d[k, i]}, {i, 1, k}] // TableForm<br> Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,<br>    k}] // TableForm<br>
+==diagonals of regular polygon==
-#  Plot[d[k, i], {i, 0, 2 k}]<br>
+* length of hepagon
+$$d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} $$
@@ 26번째 줄: / 17번째 줄: @@
 * [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<br><br>
+* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html<br> also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity

← 이전 판		2013년 12월 1일 (일) 21:44 판
54번째 줄:		54번째 줄:

	[[분류:개인노트]]		[[분류:개인노트]]
−	~~[[Category:research topics]]~~
	[[Category:quantum dimensions]]		[[Category:quantum dimensions]]

@@ 2번째 줄: / 2번째 줄: @@
 * borrowed from [[Andrews-Gordon identity]]
-*  quantum dimension and thier recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
+*  quantum dimension and thier recurrence relation
@@ 41번째 줄: / 43번째 줄: @@
 * [[sl(2) - orthogonal polynomials and Lie theory]]
@@ 74번째 줄: / 53번째 줄: @@
 ** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
 [[분류:개인노트]]
 [[Category:research topics]]
 [[Category:quantum dimensions]]