셀베르그 적분(Selberg integral) - 편집 역사

2021년 2월 17일 (수) 12:48에 Pythagoras0님의 편집

2021-02-17T12:48:39Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T14:31:13Z

메타데이터: 새 문단

2020년 11월 13일 (금) 10:19에 Pythagoras0님의 편집

2020-11-13T10:19:58Z

Pythagoras0: section '관련논문' updated

2016-05-05T09:05:27Z

section '관련논문' updated

Pythagoras0: section '리뷰, 에세이, 강의노트' updated

2016-03-10T04:34:01Z

section '리뷰, 에세이, 강의노트' updated

2015년 8월 23일 (일) 03:25에 Pythagoras0님의 편집

2015-08-23T03:25:30Z

Pythagoras0: /* 관련된 항목들 */

2015-08-23T03:09:55Z

Pythagoras0: /* 관련논문 */

2015-08-11T00:32:07Z

Pythagoras0: /* 관련된 항목들 */

2015-04-29T08:14:51Z

Pythagoras0: /* 관련논문 */

2015-04-29T08:14:22Z

@@ 65번째 줄: / 65번째 줄: @@
 [[분류:특수함수]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q7447525 Q7447525]

← 이전 판		2020년 12월 28일 (월) 14:31 판
64번째 줄:		64번째 줄:
	[[분류:적분]]		[[분류:적분]]
	[[분류:특수함수]]		[[분류:특수함수]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q7447525 Q7447525]

@@ 7번째 줄: / 7번째 줄: @@
 & = \prod_{j = 0}^{n-1}  \frac {\Gamma(\alpha + j \gamma) \Gamma(\beta + j \gamma) \Gamma (1 + (j+1)\gamma)}  {\Gamma(\alpha + \beta + (n+j-1)\gamma) \Gamma(1+\gamma)} \end{align},</math>
 여기서
-$$
+:<math>
 \Re(\alpha)>0, \Re(\beta)>0, \Re(\gamma)>\max\{-\frac{1}{n},-\frac{\Re{\alpha}}{n-1},-\frac{\Re{\beta}}{n-1}\}
-$$
+</math>
 *  n=1 인 경우
 :<math>S_{1} (\alpha, \beta,\gamma)=B(\alpha,\beta) = \int_0^1t^{\alpha-1}(1-t)^{\beta-1}\,dt</math>
@@ 19번째 줄: / 19번째 줄: @@
 * Gauge theory (supersymmetry, AGT conjecture)
 * Geometry (hyperplane arrangements)
-* Number theory (moments $\zeta(s)$
+* Number theory (moments <math>\zeta(s)</math>
 * Orthogonal polynomials (Generalised Jacobi polynomials)
 * Random matrices
@@ 47번째 줄: / 47번째 줄: @@
 ==관련논문==
-* Peter J. Forrester, Volumes for ${\rm SL}_N(\mathbb R)$, the Selberg integral and random lattices, arXiv:1604.07462 [math-ph], April 25 2016, http://arxiv.org/abs/1604.07462
+* Peter J. Forrester, Volumes for <math>{\rm SL}_N(\mathbb R)</math>, the Selberg integral and random lattices, arXiv:1604.07462 [math-ph], April 25 2016, http://arxiv.org/abs/1604.07462
 * Rosengren, Hjalmar. “Selberg Integrals, Askey-Wilson Polynomials and Lozenge Tilings of a Hexagon with a Triangular Hole.” arXiv:1503.00971 [math], March 3, 2015. http://arxiv.org/abs/1503.00971.
 * Patterson, Samuel J. “Selberg Sums - a New Perspective.” arXiv:1411.7600 [math], November 27, 2014. http://arxiv.org/abs/1411.7600.
@@ 54번째 줄: / 54번째 줄: @@
 * Zhang, Hong, and Yutaka Matsuo. ‘Selberg Integral and SU(N) AGT Conjecture’. Journal of High Energy Physics 2011, no. 12 (December 2011). doi:10.1007/JHEP12(2011)106.
 * Mironov, A., Al Morozov, and And Morozov. ‘Matrix Model Version of AGT Conjecture and Generalized Selberg Integrals’. Nuclear Physics B 843, no. 2 (February 2011): 534–57. doi:10.1016/j.nuclphysb.2010.10.016.
-* Warnaar, S. Ole. “The $\mathfrak{sl}_3$ Selberg Integral.” Advances in Mathematics 224, no. 2 (2010): 499–524. doi:10.1016/j.aim.2009.11.011.
+* Warnaar, S. Ole. “The <math>\mathfrak{sl}_3</math> Selberg Integral.” Advances in Mathematics 224, no. 2 (2010): 499–524. doi:10.1016/j.aim.2009.11.011.
-* Warnaar, S. Ole. “A Selberg Integral for the Lie Algebra $A_n$.” Acta Mathematica 203, no. 2 (2009): 269–304. doi:10.1007/s11511-009-0043-x.
+* Warnaar, S. Ole. “A Selberg Integral for the Lie Algebra <math>A_n</math>.” Acta Mathematica 203, no. 2 (2009): 269–304. doi:10.1007/s11511-009-0043-x.
 * Warnaar, S. Ole. ‘The Mukhin--Varchenko Conjecture for Type A’. DMTCS Proceedings 0, no. 1 (22 December 2008). http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAJ0108.
 * Luque, Jean-Gabriel, and Jean-Yves Thibon. “Hankel Hyperdeterminants and Selberg Integrals.” Journal of Physics A: Mathematical and General 36, no. 19 (May 16, 2003): 5267. doi:10.1088/0305-4470/36/19/306.

@@ 47번째 줄: / 47번째 줄: @@
 ==관련논문==
 * Rosengren, Hjalmar. “Selberg Integrals, Askey-Wilson Polynomials and Lozenge Tilings of a Hexagon with a Triangular Hole.” arXiv:1503.00971 [math], March 3, 2015. http://arxiv.org/abs/1503.00971.
 * Patterson, Samuel J. “Selberg Sums - a New Perspective.” arXiv:1411.7600 [math], November 27, 2014. http://arxiv.org/abs/1411.7600.

@@ 40번째 줄: / 40번째 줄: @@
 ==리뷰, 에세이, 강의노트==
 * Warnaar, [http://www.maths.adelaide.edu.au/thomas.leistner/colloquium/20110805OleWarnaar/Selberg.pdf The Selberg Integral], 2011
 * Warnaar, [http://www.maths.uq.edu.au/~uqowarna/talks/FPSAC08.pdf The Mukhin{Varchenko conjecture for type A], 2008

← 이전 판		2015년 8월 23일 (일) 03:25 판
13번째 줄:		13번째 줄:
	:<math>S_{1} (\alpha, \beta,\gamma)=B(\alpha,\beta) = \int_0^1t^{\alpha-1}(1-t)^{\beta-1}\,dt</math>		:<math>S_{1} (\alpha, \beta,\gamma)=B(\alpha,\beta) = \int_0^1t^{\alpha-1}(1-t)^{\beta-1}\,dt</math>

−
−
−
−
−
−
−	~~==역사==~~
−
−
−
−	* http://www.google.com/search?hl=en&tbs=tl:1&q=
−	* [[수학사 연표]]
−
−
−

	==메모==		==메모==

@@ 45번째 줄: / 45번째 줄: @@
 * [[타원 셀베르그 적분]]
 * [[Chowla-셀베르그 공식]]
 ==사전 형태의 자료==

@@ 68번째 줄: / 68번째 줄: @@
 * Luque, Jean-Gabriel, and Jean-Yves Thibon. “Hankel Hyperdeterminants and Selberg Integrals.” Journal of Physics A: Mathematical and General 36, no. 19 (May 16, 2003): 5267. doi:10.1088/0305-4470/36/19/306.
 * Tarasov, V., and A. Varchenko. ‘Selberg-Type Integrals Associated with SL3’. Letters in Mathematical Physics 65, no. 3 (1 September 2003): 173–85. doi:10.1023/B:MATH.0000010712.67685.9d.
 * Selberg, Atle. “Remarks on a Multiple Integral.” Norsk Mat. Tidsskr. 26 (1944): 71–78.
 [[분류:적분]]
 [[분류:특수함수]]

@@ 41번째 줄: / 41번째 줄: @@
 ==관련된 항목들==
 * [[오일러 베타적분(베타함수)|오일러 베타적분]]
 * [[맥도날드-메타 적분]]
 * [[Chowla-셀베르그 공식]]
 ==사전 형태의 자료==