슬레이터 목록 (Slater's list) - 편집 역사

2020년 12월 28일 (월) 10:39에 Pythagoras0님의 편집

2020-12-28T10:39:54Z

2020년 11월 16일 (월) 15:27에 Pythagoras0님의 편집

2020-11-16T15:27:16Z

2020년 11월 12일 (목) 15:12에 Pythagoras0님의 편집

2020-11-12T15:12:29Z

2013년 5월 13일 (월) 09:30에 Pythagoras0님의 편집

2013-05-13T09:30:11Z

2013년 3월 11일 (월) 22:10에 Pythagoras0님의 편집

2013-03-11T22:10:25Z

2013년 2월 13일 (수) 22:34에 Pythagoras0님의 편집

2013-02-13T22:34:22Z

Pythagoras0: 찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

2013-01-15T01:33:24Z

찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

Pythagoras0: 찾아 바꾸기 – “
$” 문자열을 “: ” 문자열로$

2013-01-12T17:56:54Z

찾아 바꾸기 – “<br><math>” 문자열을 “:<math>” 문자열로

Pythagoras0: 찾아 바꾸기 – “==관련도서== * 도서내검색
http://books.google.com/books?q= http://book.daum.net/search/contentSearch.do?query=” 문자열을 “” 문자열로

2012-11-02T15:28:14Z

찾아 바꾸기 – “==관련도서== * 도서내검색<br> ** http://books.google.com/books?q= ** http://book.daum.net/search/contentSearch.do?query=” 문자열을 “” 문자열로

Pythagoras0: 찾아 바꾸기 – “

” 문자열을 “==” 문자열로

2012-11-01T21:28:13Z

찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
-−
-−
 ==주요 항등식==
-* '''[Slater51] '''(1.3)
+* '''[Slater51] '''(1.3)
-* '''[Slater51] '''(2.1)
+* '''[Slater51] '''(2.1)
-* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
+* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
-* '''[Slater51] '''(4.2):<math>\sum_{r=-[n/2]}^{r=[n/2]}\frac{(1-aq^{4r})(q^{-n})_{2r}a^{2r}q^{2nr+r}(d)_{q^2,r}(e)_{q^2,r}}{(1-a)(aq^{n+1})_{2r}d^re^r(aq^2/d)_{q^2,r}(aq^2/e)_{q^2,r}}=\frac{(q^2/a,aq/d,aq/e,aq^2/de;q^2)_{\infty}}{(q,q^2/d,q^2/e,a^2q/de;q^2)_{\infty}}\frac{(q)_{n}(aq)_{n}(a^2/de)_{q^2,n}}{(aq)_{q^2,n}(aq/d)_{n}(aq/e)_{n}}</math>
+* '''[Slater51] '''(4.2):<math>\sum_{r=-[n/2]}^{r=[n/2]}\frac{(1-aq^{4r})(q^{-n})_{2r}a^{2r}q^{2nr+r}(d)_{q^2,r}(e)_{q^2,r}}{(1-a)(aq^{n+1})_{2r}d^re^r(aq^2/d)_{q^2,r}(aq^2/e)_{q^2,r}}=\frac{(q^2/a,aq/d,aq/e,aq^2/de;q^2)_{\infty}}{(q,q^2/d,q^2/e,a^2q/de;q^2)_{\infty}}\frac{(q)_{n}(aq)_{n}(a^2/de)_{q^2,n}}{(aq)_{q^2,n}(aq/d)_{n}(aq/e)_{n}}</math>
-* '''[Slater51] '''(4.3)
+* '''[Slater51] '''(4.3)
-−
-−
 ==Group B==
-* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
+* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
 *  B(1)
 ** [[슬레이터 18]]
@@ 25번째 줄: / 25번째 줄: @@
 ** [[슬레이터 14]]
-−
-−
-−
 ==Group E==
@@ 36번째 줄: / 36번째 줄: @@
 * E(2) [[슬레이터 3]]
-−
-−
 ==Group H==
-*   '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
+*   '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
 * [[슬레이터 1]]
-−
-−
 ==슬레이터 목록==
@@ 56번째 줄: / 56번째 줄: @@
 * [[슬레이터 8]]:<math>\sum_{n=0}^{\infty}\frac{(q^2;q^2)_{n}q^{n(n+1)/2}}{ (q)_{n}^2}=\frac{(-q)_{\infty}}{(q^2;q^4)_{\infty}}</math>
-−
-−
 ==메모==
-−
 * Math Overflow http://mathoverflow.net/search?q=
-−
-−
 ==관련된 항목들==
@@ 76번째 줄: / 76번째 줄: @@
-−
-−
 ==리뷰논문, 에세이, 강의노트==
-−
-−
-−
 ==관련논문==
 * McLaughlin, Sills, Zimmer [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities], 2008
 * '''[Slater52]'''Slater, L. J.[http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]Proc. London Math. Soc.1952s2-54: 147–167
-* '''[Slater51]'''Slater, L. J. [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]Proc. London Math. Soc. 1951 s2-53: 460-475
+* '''[Slater51]'''Slater, L. J. [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]Proc. London Math. Soc. 1951 s2-53: 460-475
-−
-−
 [[분류:슬레이터 목록]]
 [[분류:q-급수]]

← 이전 판		2020년 11월 16일 (월) 15:27 판
55번째 줄:		55번째 줄:
	* [[슬레이터 2]]:<math>\prod_{n=1}^{\infty}(1+q^n)=\sum_{n=1}^{\infty}\frac{q^{n(n+1)/2}}{(q)_n}</math>		* [[슬레이터 2]]:<math>\prod_{n=1}^{\infty}(1+q^n)=\sum_{n=1}^{\infty}\frac{q^{n(n+1)/2}}{(q)_n}</math>
	* [[슬레이터 8]]:<math>\sum_{n=0}^{\infty}\frac{(q^2;q^2)_{n}q^{n(n+1)/2}}{ (q)_{n}^2}=\frac{(-q)_{\infty}}{(q^2;q^4)_{\infty}}</math>		* [[슬레이터 8]]:<math>\sum_{n=0}^{\infty}\frac{(q^2;q^2)_{n}q^{n(n+1)/2}}{ (q)_{n}^2}=\frac{(-q)_{\infty}}{(q^2;q^4)_{\infty}}</math>
−
−
−
−
−
−	~~==역사==~~
−
−
−
−	* http://www.google.com/search?hl=en&tbs=tl:1&q=
−	* [[수학사 연표]]

@@ 9번째 줄: / 9번째 줄: @@
 * '''[Slater51] '''(1.3)
 * '''[Slater51] '''(2.1)
-* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math><br>
+* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
-* '''[Slater51] '''(4.2):<math>\sum_{r=-[n/2]}^{r=[n/2]}\frac{(1-aq^{4r})(q^{-n})_{2r}a^{2r}q^{2nr+r}(d)_{q^2,r}(e)_{q^2,r}}{(1-a)(aq^{n+1})_{2r}d^re^r(aq^2/d)_{q^2,r}(aq^2/e)_{q^2,r}}=\frac{(q^2/a,aq/d,aq/e,aq^2/de;q^2)_{\infty}}{(q,q^2/d,q^2/e,a^2q/de;q^2)_{\infty}}\frac{(q)_{n}(aq)_{n}(a^2/de)_{q^2,n}}{(aq)_{q^2,n}(aq/d)_{n}(aq/e)_{n}}</math><br>
+* '''[Slater51] '''(4.2):<math>\sum_{r=-[n/2]}^{r=[n/2]}\frac{(1-aq^{4r})(q^{-n})_{2r}a^{2r}q^{2nr+r}(d)_{q^2,r}(e)_{q^2,r}}{(1-a)(aq^{n+1})_{2r}d^re^r(aq^2/d)_{q^2,r}(aq^2/e)_{q^2,r}}=\frac{(q^2/a,aq/d,aq/e,aq^2/de;q^2)_{\infty}}{(q,q^2/d,q^2/e,a^2q/de;q^2)_{\infty}}\frac{(q)_{n}(aq)_{n}(a^2/de)_{q^2,n}}{(aq)_{q^2,n}(aq/d)_{n}(aq/e)_{n}}</math>
 * '''[Slater51] '''(4.3)
@@ 19번째 줄: / 19번째 줄: @@
 ==Group B==
-* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math><br>
+* '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
-*  B(1)<br>
+*  B(1)
 ** [[슬레이터 18]]
-*  B(2)<br>
+*  B(2)
 ** [[슬레이터 14]]
@@ 42번째 줄: / 42번째 줄: @@
 ==Group H==
-*   '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math><br>
+*   '''[Slater51] '''(4.1):<math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math>
 * [[슬레이터 1]]
@@ 52번째 줄: / 52번째 줄: @@
 ==슬레이터 목록==
-* [[슬레이터 1]]:<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n=1}^{\infty}(-1)^{n}(q^{\frac{3 n^2-n}{2}}+q^{\frac{3 n^2+n}{2}})=\sum_{n=-\infty}^\infty(-1)^nq^{n(3n-1)/2}</math><br>
+* [[슬레이터 1]]:<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n=1}^{\infty}(-1)^{n}(q^{\frac{3 n^2-n}{2}}+q^{\frac{3 n^2+n}{2}})=\sum_{n=-\infty}^\infty(-1)^nq^{n(3n-1)/2}</math>
-* [[슬레이터 2]]:<math>\prod_{n=1}^{\infty}(1+q^n)=\sum_{n=1}^{\infty}\frac{q^{n(n+1)/2}}{(q)_n}</math><br>
+* [[슬레이터 2]]:<math>\prod_{n=1}^{\infty}(1+q^n)=\sum_{n=1}^{\infty}\frac{q^{n(n+1)/2}}{(q)_n}</math>
-* [[슬레이터 8]]:<math>\sum_{n=0}^{\infty}\frac{(q^2;q^2)_{n}q^{n(n+1)/2}}{ (q)_{n}^2}=\frac{(-q)_{\infty}}{(q^2;q^4)_{\infty}}</math><br>
+* [[슬레이터 8]]:<math>\sum_{n=0}^{\infty}\frac{(q^2;q^2)_{n}q^{n(n+1)/2}}{ (q)_{n}^2}=\frac{(-q)_{\infty}}{(q^2;q^4)_{\infty}}</math>
@@ 101번째 줄: / 101번째 줄: @@
 ==관련논문==
 * McLaughlin, Sills, Zimmer [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities], 2008
-* '''[Slater52]'''Slater, L. J.[http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]<br>Proc. London Math. Soc.<br>1952s2-54: 147–167<br>
+* '''[Slater52]'''Slater, L. J.[http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]Proc. London Math. Soc.1952s2-54: 147–167
-* '''[Slater51]'''Slater, L. J. [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]Proc. London Math. Soc. 1951 s2-53: 460-475<br>
+* '''[Slater51]'''Slater, L. J. [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]Proc. London Math. Soc. 1951 s2-53: 460-475

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
@@ 91번째 줄: / 85번째 줄: @@
 * [[자코비 삼중곱(Jacobi triple product)]]
@@ 134번째 줄: / 100번째 줄: @@
 ==관련논문==
+* McLaughlin, Sills, Zimmer [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities], 2008
 * '''[Slater52]'''Slater, L. J.[http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]<br>Proc. London Math. Soc.<br>1952s2-54: 147–167<br>
 * '''[Slater51]'''Slater, L. J. [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]Proc. London Math. Soc. 1951 s2-53: 460-475<br>

← 이전 판		2013년 3월 11일 (월) 22:10 판
146번째 줄:		146번째 줄:

	[[분류:슬레이터 목록]]		[[분류:슬레이터 목록]]
		+	[[분류:q-급수]]

← 이전 판	2013년 2월 13일 (수) 22:34 판
145번째 줄:	145번째 줄:


	+	[[분류:슬레이터 목록]]

← 이전 판		2013년 1월 15일 (화) 01:33 판
71번째 줄:		71번째 줄:

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

← 이전 판		2012년 11월 2일 (금) 15:28 판
145번째 줄:		145번째 줄:


−
−	~~==관련도서==~~
−
−	* 도서내검색<br>
−	** http://books.google.com/books?q=
−	** http://book.daum.net/search/contentSearch.do?query=

@@ 1번째 줄: / 1번째 줄: @@
-<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 수학노트 원문주소==
+==이 항목의 수학노트 원문주소==
@@ 46번째 줄: / 46번째 줄: @@
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">Group H==
+==Group H==
 *   '''[Slater51] '''(4.1)<br><math>\sum_{r=0}^{n}\frac{(1-aq^{2r})(-1)^{r}q^{\frac{1}{2}(r^2+r)}(a)_{r}(c)_{r}(d)_{r}a^{r}}{(a)_{n+r+1}(q)_{n-r}(q)_{r}(aq/c)_{r}(aq/d)_{r}c^{r}d^{r}}=\frac{(aq/cd)_{n}}{(q)_{n}(aq/c)_{n}(aq/d)_{n}}</math><br>
@@ 95번째 줄: / 95번째 줄: @@
-<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역==
+==수학용어번역==
 *  단어사전<br>