Slater 92 - 편집 역사

2020년 12월 28일 (월) 12:02에 Pythagoras0님의 편집

2020-12-28T12:02:30Z

Pythagoras0: /* articles */

2020-12-28T07:08:03Z

articles

2020년 12월 28일 (월) 07:05에 Pythagoras0님의 편집

2020-12-28T07:05:20Z

2020년 11월 16일 (월) 10:12에 Pythagoras0님의 편집

2020-11-16T10:12:52Z

2020년 11월 14일 (토) 19:38에 Pythagoras0님의 편집

2020-11-14T19:38:01Z

2020년 11월 13일 (금) 07:39에 Pythagoras0님의 편집

2020-11-13T07:39:23Z

2020년 11월 13일 (금) 05:34에 imported>Pythagoras0님의 편집

2020-11-13T05:34:13Z

imported>Pythagoras0: 찾아 바꾸기 – “4909919” 문자열을 “” 문자열로

2012-11-02T12:46:42Z

찾아 바꾸기 – “4909919” 문자열을 “” 문자열로

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

2012-10-29T17:55:55Z

imported>Pythagoras0: 찾아 바꾸기 – “\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}” 문자열을 “\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}

2012-10-29T14:46:41Z

찾아 바꾸기 – “\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}” 문자열을 “\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}

@@ 2번째 줄: / 2번째 줄: @@
 * [[twisted Chebyshev polynomials and dilogarithm identities|an explanation for dilogarithm ladder]][[twisted Chebyshev polynomials and dilogarithm identities|twisted Chebyshev polynomials and dilogarithm identities]]
-*  Loxton & Lewin<math>x, -y, -z^{-1}</math>가 방정식 <math>x^3+3x^2-1=0</math>의 해라고 하자.<math>3L(x^3)-9L(x^2)-9L(x)+7L(1)=0</math><math>3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0</math><math>3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0</math>
+*  Loxton & Lewin<math>x, -y, -z^{-1}</math>가 방정식 <math>x^3+3x^2-1=0</math>의 해라고 하자.<math>3L(x^3)-9L(x^2)-9L(x)+7L(1)=0</math><math>3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0</math><math>3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0</math>
-−
-−
 ==type of identity==
@@ 13번째 줄: / 13번째 줄: @@
 *  B(3)
-−
-−
 ==Bailey pair 1==
-*  Use the folloing<math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math>,  <math>\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}</math>
+*  Use the folloing<math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math>,  <math>\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}</math>
 *  Specialize<math>x=q^2, y=-q, z\to\infty</math>.
 *  Bailey pair<math>\delta_n=(-q)_{n}q^{\frac{n(n+1)}{2}}</math><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</math>
-−
-−
 ==Bailey pair 2==
-*  Use the following <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>
+*  Use the following <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>
 *  Specialize<math>a=q,c=-q,d=\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}q^{\frac{n(n+1)}{2}}</math><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</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==
@@ 49번째 줄: / 49번째 줄: @@
 <math>\sum_{n=0}^{\infty}\frac{(q^3;q^3)_{n}q^{n(n+1)}}{ (q)_{n}(q;q^{2})_n(q^2;q^2)_{n}}=\frac{(q^{9};q^{27})_{\infty}(q^{18};q^{27})_{\infty}(q^{27};q^{27})_{\infty}}{(q)_{\infty}}</math>
-−
 * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 ** 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>
-−
 a=2,d_1=1,d_2=2,d_3=2,e_1=e_2=e_3=1
-−
 <math>\frac{(1-x)(1-x^2)^2}{(1-x^3)}=x^2</math>
@@ 79번째 줄: / 79번째 줄: @@
 <math>x^3+3x^2-1=0</math>
-<math>x, -y, -z^{-1}</math>가 방정식 의 해 [http://www.wolframalpha.com/input/?i=x%5E3%2B3x%5E2-1%3D0 http://www.wolframalpha.com/input/?i=x^3%2B3x^2-1%3D0]
+<math>x, -y, -z^{-1}</math>가 방정식 의 해 [http://www.wolframalpha.com/input/?i=x%5E3%2B3x%5E2-1%3D0 http://www.wolframalpha.com/input/?i=x^3%2B3x^2-1%3D0]
-−
-−
 ==dilogarithm identity==
@@ 89번째 줄: / 89번째 줄: @@
 <math>L(x^3)-3L(x^2)-3L(x)=-\frac{7}{3}L(1)</math>
-−
-−
 ==related items==
-−
-−
-−
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 101번째 줄: / 101번째 줄: @@
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 108번째 줄: / 108번째 줄: @@
 * [http://www.zentralblatt-math.org/zmath/en/ ]http://www.zentralblatt-math.org/zmath/en/
 * [http://arxiv.org/ ]http://arxiv.org/
 * http://dx.doi.org/

← 이전 판		2020년 11월 16일 (월) 10:12 판
96번째 줄:		96번째 줄:


−
−
−
−
−
−	~~==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=
−
−

@@ 124번째 줄: / 124번째 줄: @@
 * [http://arxiv.org/ ]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/
+*

@@ 1번째 줄: / 1번째 줄: @@
 ==Note==
-* [[twisted Chebyshev polynomials and dilogarithm identities|an explanation for dilogarithm ladder]]<br>[[twisted Chebyshev polynomials and dilogarithm identities|twisted Chebyshev polynomials and dilogarithm identities]]<br>
+* [[twisted Chebyshev polynomials and dilogarithm identities|an explanation for dilogarithm ladder]][[twisted Chebyshev polynomials and dilogarithm identities|twisted Chebyshev polynomials and dilogarithm identities]]
-*  Loxton & Lewin<br><math>x, -y, -z^{-1}</math>가 방정식 <math>x^3+3x^2-1=0</math>의 해라고 하자.<br><math>3L(x^3)-9L(x^2)-9L(x)+7L(1)=0</math><br><math>3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0</math><br><math>3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0</math><br>
+*  Loxton & Lewin<math>x, -y, -z^{-1}</math>가 방정식 <math>x^3+3x^2-1=0</math>의 해라고 하자.<math>3L(x^3)-9L(x^2)-9L(x)+7L(1)=0</math><math>3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0</math><math>3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0</math>
@@ 11번째 줄: / 11번째 줄: @@
 * [[Slater list|Slater's list]]
-*  B(3)<br>
+*  B(3)
@@ 19번째 줄: / 19번째 줄: @@
 ==Bailey pair 1==
-*  Use the folloing<br><math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math>,  <math>\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}</math><br>
+*  Use the folloing<math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math>,  <math>\gamma_n=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}</math>
-*  Specialize<br><math>x=q^2, y=-q, z\to\infty</math>.<br>
+*  Specialize<math>x=q^2, y=-q, z\to\infty</math>.
-*  Bailey pair<br><math>\delta_n=(-q)_{n}q^{\frac{n(n+1)}{2}}</math><br><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</math><br>
+*  Bailey pair<math>\delta_n=(-q)_{n}q^{\frac{n(n+1)}{2}}</math><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</math>
@@ 29번째 줄: / 29번째 줄: @@
 ==Bailey pair 2==
-*  Use the following <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>
+*  Use the following <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>
-*  Specialize<br><math>a=q,c=-q,d=\infty</math><br>
+*  Specialize<math>a=q,c=-q,d=\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>
@@ 39번째 줄: / 39번째 줄: @@
 ==Bailey pair ==
-*  Bailey pairs<br><math>\delta_n=(-q)_{n}q^{\frac{n(n+1)}{2}}</math><br><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</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>
+*  Bailey pairs<math>\delta_n=(-q)_{n}q^{\frac{n(n+1)}{2}}</math><math>\gamma_n=\frac{(-q)_{\infty}}{(q^2)_{\infty}}q^{\frac{n(n+1)}{2}}</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>
@@ 51번째 줄: / 51번째 줄: @@
-* [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=
@@ 105번째 줄: / 105번째 줄: @@
-* [[2010년 books and articles]]<br>
+* [[2010년 books and articles]]
 * http://gigapedia.info/1/
 * http://gigapedia.info/1/

← 이전 판		2020년 11월 13일 (금) 05:34 판
129번째 줄:		129번째 줄:
	[[분류:개인노트]]		[[분류:개인노트]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

← 이전 판		2012년 11월 2일 (금) 12:46 판
110번째 줄:		110번째 줄:
	* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=		* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

−	~~[[4909919\|4909919]]~~	+

← 이전 판		2012년 10월 29일 (월) 17:55 판
128번째 줄:		128번째 줄:
	*		*
	[[분류:개인노트]]		[[분류:개인노트]]
		+	[[분류:math and physics]]