Slater 31 - 편집 역사

2020년 12월 28일 (월) 12:06에 Pythagoras0님의 편집

2020-12-28T12:06:40Z

2020년 11월 16일 (월) 10:34에 Pythagoras0님의 편집

2020-11-16T10:34:39Z

2020년 11월 16일 (월) 10:26에 Pythagoras0님의 편집

2020-11-16T10:26:23Z

2020년 11월 16일 (월) 09:51에 Pythagoras0님의 편집

2020-11-16T09:51:32Z

2020년 11월 13일 (금) 09:44에 Pythagoras0님의 편집

2020-11-13T09:44:26Z

2020년 11월 13일 (금) 09:42에 imported>Pythagoras0님의 편집

2020-11-13T09:42:25Z

2020년 11월 13일 (금) 09:42에 imported>Pythagoras0님의 편집

2020-11-13T09:42:21Z

2012년 10월 29일 (월) 17:55에 imported>Pythagoras0님의 편집

2012-10-29T17:55:54Z

imported>Pythagoras0: 찾아 바꾸기 – “

” 문자열을 “==” 문자열로

2012-10-29T00:47:31Z

찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로

2012년 10월 29일 (월) 00:03에 imported>Pythagoras0님의 편집

2012-10-29T00:03:44Z

@@ 3번째 줄: / 3번째 줄: @@
 * [[Rogers-Selberg identities]]<math>C(q)=\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math>
-−
 <math>C(q)=\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math>
-−
-−
 ==Bailey pair 2==
-*  Use the following <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>
+*  Use the following <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>
 *  Specialize<math>a=q,d=-q^{\frac{3}{2}},e=\infty</math>
-*  Bailey pair<math>\alpha_{0}=1</math>, <math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><math>\beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(x)_{n-r}(q)_{n+r}}=\sum_{r=0}^{n}\frac{\alpha_r}{(q^{2})_{n-r}(q)_{n+r}}=\frac{1}{(q)_{n}(-q)_{n}}</math>
+*  Bailey pair<math>\alpha_{0}=1</math>, <math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><math>\beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(x)_{n-r}(q)_{n+r}}=\sum_{r=0}^{n}\frac{\alpha_r}{(q^{2})_{n-r}(q)_{n+r}}=\frac{1}{(q)_{n}(-q)_{n}}</math>
-−
-−
-==Bailey pair ==
+==Bailey pair ==
 *  Bailey pairs<math>\delta_n=q^{n^2}</math><math>\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}</math><math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><math>\beta_n=\frac{1}{(q)_{n}(-q)_{n}}</math>
-−
 ==q-series identity==
@@ 36번째 줄: / 36번째 줄: @@
 ** http://www.research.att.com/~njas/sequences/?q=
-−
-−
 ==Bethe type equation (cyclotomic equation)==
-Let <math>\sum_{n=0}^{\infty}\frac{q^{n(an+b)/2}}{
+Let <math>\sum_{n=0}^{\infty}\frac{q^{n(an+b)/2}}{
   \prod_{j=1}^{r}(q^{c_j};q^{d_j})_n^{e_j}}=\sum_{N=0}^{\infty} a_N q^{N}</math>.
-Then <math>\prod_{j=1}^{r}(1-x^{d_j})^{e_j}=x^a</math>  has a unique root <math>0<\mu<1</math>. We get
+Then <math>\prod_{j=1}^{r}(1-x^{d_j})^{e_j}=x^a</math>  has a unique root <math>0<\mu<1</math>. We get
 <math>\log^2 a_N \sim 4N\sum_{j=1}^{r}\frac{e_j}{d_j}L(1-\mu^{d_j})</math>
@@ 57번째 줄: / 57번째 줄: @@
 a=4,d1=4,e1=1,d2=4,e2=1,d3=2,e3=-1
-The equation  becomes <math>(1-x^4)(1-x^4)=x^4(1-x^2)</math>.
+The equation  becomes <math>(1-x^4)(1-x^4)=x^4(1-x^2)</math>.
 This is factorized into <math>(-1+x) (1+x) \left(-1-x^2+2 x^4+x^6\right)</math>
@@ 69번째 줄: / 69번째 줄: @@
 <math>7L(\alpha^2)-7L(\alpha)+L(1)=0</math>
-−
-−
-−
 ==dilogarithm identity==
@@ 79번째 줄: / 79번째 줄: @@
 <math>7L(\alpha^2)-7L(\alpha)+L(1)=0</math> where <math>\alpha=\frac{\sec\frac{2\pi}{7}}{2}=0.80194\cdots</math>
-−
-−
-−
 ==related items==
@@ 89번째 줄: / 89번째 줄: @@
 * [[asymptotic analysis of basic hypergeometric series]]
-−
-−
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 93번째 줄: / 93번째 줄: @@
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:migrate]]

← 이전 판		2020년 11월 16일 (월) 10:26 판
88번째 줄:		88번째 줄:

	* [[asymptotic analysis of basic hypergeometric series]]		* [[asymptotic analysis of basic hypergeometric series]]
−
−
−
−
−
−	~~==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=

@@ 113번째 줄: / 113번째 줄: @@
 * http://arxiv.org/
 * http://pythagoras0.springnote.com/
-* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 * http://dx.doi.org/
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 1번째 줄: / 1번째 줄: @@
 ==Note==
-* [[Rogers-Selberg identities]]<br><math>C(q)=\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math><br>
+* [[Rogers-Selberg identities]]<math>C(q)=\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math>
@@ 13번째 줄: / 13번째 줄: @@
 ==Bailey pair 2==
-*  Use the following <br><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>
+*  Use the following <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>
-*  Specialize<br><math>a=q,d=-q^{\frac{3}{2}},e=\infty</math><br>
+*  Specialize<math>a=q,d=-q^{\frac{3}{2}},e=\infty</math>
-*  Bailey pair<br><math>\alpha_{0}=1</math>, <math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><br><math>\beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(x)_{n-r}(q)_{n+r}}=\sum_{r=0}^{n}\frac{\alpha_r}{(q^{2})_{n-r}(q)_{n+r}}=\frac{1}{(q)_{n}(-q)_{n}}</math><br>
+*  Bailey pair<math>\alpha_{0}=1</math>, <math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><math>\beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(x)_{n-r}(q)_{n+r}}=\sum_{r=0}^{n}\frac{\alpha_r}{(q^{2})_{n-r}(q)_{n+r}}=\frac{1}{(q)_{n}(-q)_{n}}</math>
@@ 23번째 줄: / 23번째 줄: @@
 ==Bailey pair ==
-*  Bailey pairs<br><math>\delta_n=q^{n^2}</math><br><math>\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}</math><br><math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><br><math>\beta_n=\frac{1}{(q)_{n}(-q)_{n}}</math><br>  <br>
+*  Bailey pairs<math>\delta_n=q^{n^2}</math><math>\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}</math><math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><math>\beta_n=\frac{1}{(q)_{n}(-q)_{n}}</math>
@@ 31번째 줄: / 31번째 줄: @@
 <math>\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math>
-* [[Bailey pair and lemma|Bailey's lemma]]<br><math>\sum_{n=0}^{\infty}\alpha_n\gamma_{n}=\sum_{n=0}^{\infty}\beta_n\delta_{n}</math><br><math>\sum_{n=0}^{\infty}\beta_n\delta_{n}=\sum_{n=0}^{\infty}\frac{q^{n^2}}{(q)_{n}}</math><br><math>\sum_{n=0}^{\infty}\alpha_n\gamma_{n}=\frac{(-q)_{\infty}}{(q)_{\infty}}\sum_{n=0}^{\infty}(-1)^{n}(q^{\frac{3n^2+n}{2}}-q^{\frac{3n^2+5n+2}{2}})=(-q)_{\infty}</math><br>
+* [[Bailey pair and lemma|Bailey's lemma]]<math>\sum_{n=0}^{\infty}\alpha_n\gamma_{n}=\sum_{n=0}^{\infty}\beta_n\delta_{n}</math><math>\sum_{n=0}^{\infty}\beta_n\delta_{n}=\sum_{n=0}^{\infty}\frac{q^{n^2}}{(q)_{n}}</math><math>\sum_{n=0}^{\infty}\alpha_n\gamma_{n}=\frac{(-q)_{\infty}}{(q)_{\infty}}\sum_{n=0}^{\infty}(-1)^{n}(q^{\frac{3n^2+n}{2}}-q^{\frac{3n^2+5n+2}{2}})=(-q)_{\infty}</math>
-* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>
+* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 ** http://www.research.att.com/~njas/sequences/?q=
@@ 87번째 줄: / 87번째 줄: @@
 ==related items==
-* [[asymptotic analysis of basic hypergeometric series]]<br>
+* [[asymptotic analysis of basic hypergeometric series]]
@@ 97번째 줄: / 97번째 줄: @@
-* [[2010년 books and articles]]<br>
+* [[2010년 books and articles]]
 * http://gigapedia.info/1/
 * http://gigapedia.info/1/
@@ 108번째 줄: / 108번째 줄: @@
 ==articles==
-*   <br>
 * http://www.ams.org/mathscinet
 * http://www.zentralblatt-math.org/zmath/en/

← 이전 판		2020년 11월 13일 (금) 09:42 판
91번째 줄:		91번째 줄:


		+
		+
		+	==books==
		+
		+
		+
		+	* [[2010년 books and articles]]<br>
		+	* http://gigapedia.info/1/
		+	* http://gigapedia.info/1/
		+	* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
		+
		+
		+
		+
		+
		+	==articles==
		+
		+	* <br>
		+	* http://www.ams.org/mathscinet
		+	* http://www.zentralblatt-math.org/zmath/en/
		+	* http://arxiv.org/
		+	* http://pythagoras0.springnote.com/
		+	* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
		+	* http://dx.doi.org/
	[[분류:개인노트]]		[[분류:개인노트]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

← 이전 판		2012년 10월 29일 (월) 17:55 판
116번째 줄:		116번째 줄:
	* http://dx.doi.org/		* http://dx.doi.org/
	[[분류:개인노트]]		[[분류:개인노트]]
		+	[[분류:math and physics]]

@@ 11번째 줄: / 11번째 줄: @@
-<h5 style="line-height: 2em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">Bailey pair 2==
+==Bailey pair 2==
 *  Use the following <br><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>
@@ 21번째 줄: / 21번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">Bailey pair ==
+==Bailey pair ==
 *  Bailey pairs<br><math>\delta_n=q^{n^2}</math><br><math>\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}</math><br><math>\alpha_{n}=(-1)^{n}q^{n^2}(1-q^{2n+1})/(1-q)</math><br><math>\beta_n=\frac{1}{(q)_{n}(-q)_{n}}</math><br>  <br>
@@ 27번째 줄: / 27번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">q-series identity==
+==q-series identity==
 <math>\sum_{n=0}^{\infty}\frac{q^{2n^2+2n}}{ (q^{2};q^{2})_{n}(-q;q)_{2n+1}}=\frac{(q^{1};q^{7})_{\infty}(q^{6};q^{7})_{\infty}(q^{7};q^{7})_{\infty}}{(q^{2};q^{2})_{\infty}}</math>
@@ 40번째 줄: / 40번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">Bethe type equation (cyclotomic equation)==
+==Bethe type equation (cyclotomic equation)==
 Let <math>\sum_{n=0}^{\infty}\frac{q^{n(an+b)/2}}{
@@ 75번째 줄: / 75번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">dilogarithm identity==
+==dilogarithm identity==
 <math>7L(\alpha^2)-7L(\alpha)+L(1)=0</math> where <math>\alpha=\frac{\sec\frac{2\pi}{7}}{2}=0.80194\cdots</math>
@@ 85번째 줄: / 85번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items==
+==related items==
 * [[asymptotic analysis of basic hypergeometric series]]<br>
@@ 93번째 줄: / 93번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books==
+==books==
@@ 106번째 줄: / 106번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles==
+==articles==
 *   <br>

← 이전 판		2012년 10월 29일 (월) 00:03 판
115번째 줄:		115번째 줄:
	* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]		* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
	* http://dx.doi.org/		* http://dx.doi.org/
		+	[[분류:개인노트]]