5th order mock theta functions - 편집 역사

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← 이전 판	2020년 11월 13일 (금) 07:11 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	:<math>f_0(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_{n}}</math>
	+	:<math>f_1(q) = \sum_{n\ge 0} {q^{n^2+n}\over (-q;q)_{n}}</math>
	+	:<math>\phi_0(q) = \sum_{n\ge 0} {q^{n^2}(-q;q^2)_{n}}</math>
	+	:<math>\phi_1(q) = \sum_{n\ge 0} {q^{(n+1)^2}(-q;q)_{n}}</math>
	+	:<math>\psi_0(q) = \sum_{n\ge 0} {q^{(n+1)(n+2)/2}(-q;q)_{n}}</math>
	+	:<math>\psi_1(q) = \sum_{n\ge 0} {q^{n(n+1)/2}(-q;q)_{n}}</math>
	+	:<math>\chi_0(q) = \sum_{n\ge 0} {q^{n}\over (q^{n+1};q)_{n}} = 2F_0(q)-\phi_0(-q)</math>
	+	:<math>\chi_1(q) = \sum_{n\ge 0} {q^{n}\over (q^{n+1};q)_{n+1}} = 2F_1(q)+q^{-1}\phi_1(-q)</math>
	+	:<math>F_0(q) = \sum_{n\ge 0} {q^{2n^2}\over (q;q^2)_{n}}</math>
	+	:<math>F_1(q) = \sum_{n\ge 0} {q^{2n^2+2n}\over (q;q^2)_{n+1}}</math>
	+	:<math>\Psi_0(q) = -1 + \sum_{n \ge 0} { q^{5n^2}\over(1-q)(1-q^4)(1-q^6)(1-q^9)...(1-q^{5n+1})}</math>
	+	:<math>\Psi_1(q) = -1 + \sum_{n \ge 0} { q^{5n^2}\over(1-q^2)(1-q^3)(1-q^7)(1-q^8)...(1-q^{5n+2}) }</math>
	+

	+	==related items==
	+	* [[WRT (Witten-Reshetikhin-Turaev) invariant]]
	+
	+
	+	==articles==
	+	* Nickolas Andersen, Vector-valued modular forms and the Mock Theta Conjectures, arXiv:1604.05294 [math.NT], April 18 2016, http://arxiv.org/abs/1604.05294
	+	* G.E. Andrews, [http://www.jstor.org/stable/2000275 The fifth and seventh order mock theta functions]. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
	+	* <cite class="" id="CITEREFAndrews1988" style="line-height: 2em; font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="line-height: 2em;">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>
	+	* Basil Gordon and Richard J. Mcintosh [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions], 2003
	+
	+	[[분류:개인노트]]
	+	[[분류:math and physics]]
	+	[[분류:mock modular forms]]
	+	[[분류:math]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 13일 (금) 07:11 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	~~:<math>f_0(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_{n}}</math>~~
−	~~:<math>f_1(q) = \sum_{n\ge 0} {q^{n^2+n}\over (-q;q)_{n}}</math>~~
−	~~:<math>\phi_0(q) = \sum_{n\ge 0} {q^{n^2}(-q;q^2)_{n}}</math>~~
−	~~:<math>\phi_1(q) = \sum_{n\ge 0} {q^{(n+1)^2}(-q;q)_{n}}</math>~~
−	~~:<math>\psi_0(q) = \sum_{n\ge 0} {q^{(n+1)(n+2)/2}(-q;q)_{n}}</math>~~
−	~~:<math>\psi_1(q) = \sum_{n\ge 0} {q^{n(n+1)/2}(-q;q)_{n}}</math>~~
−	~~:<math>\chi_0(q) = \sum_{n\ge 0} {q^{n}\over (q^{n+1};q)_{n}} = 2F_0(q)-\phi_0(-q)</math>~~
−	~~:<math>\chi_1(q) = \sum_{n\ge 0} {q^{n}\over (q^{n+1};q)_{n+1}} = 2F_1(q)+q^{-1}\phi_1(-q)</math>~~
−	~~:<math>F_0(q) = \sum_{n\ge 0} {q^{2n^2}\over (q;q^2)_{n}}</math>~~
−	~~:<math>F_1(q) = \sum_{n\ge 0} {q^{2n^2+2n}\over (q;q^2)_{n+1}}</math>~~
−	~~:<math>\Psi_0(q) = -1 + \sum_{n \ge 0} { q^{5n^2}\over(1-q)(1-q^4)(1-q^6)(1-q^9)...(1-q^{5n+1})}</math>~~
−	~~:<math>\Psi_1(q) = -1 + \sum_{n \ge 0} { q^{5n^2}\over(1-q^2)(1-q^3)(1-q^7)(1-q^8)...(1-q^{5n+2}) }</math>~~
−

−	~~==related items==~~
−	* [[WRT (Witten-Reshetikhin-Turaev) invariant]]
−
−
−	~~==articles==~~
−	* Nickolas Andersen, Vector-valued modular forms and the Mock Theta Conjectures, arXiv:1604.05294 [math.NT], April 18 2016, http://arxiv.org/abs/1604.05294
−	* G.E. Andrews, [http://www.jstor.org/stable/2000275 The fifth and seventh order mock theta functions]. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
−	* <cite class="" id="CITEREFAndrews1988" style="line-height: 2em; font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="line-height: 2em;">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>
−	* Basil Gordon and Richard J. Mcintosh [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions], 2003
−
−	~~[[분류:개인노트]]~~
−	~~[[분류:math and physics]]~~
−	~~[[분류:mock modular forms]]~~
−	~~[[분류:math]]~~

@@ 19번째 줄: / 19번째 줄: @@
 ==articles==
 * G.E. Andrews, [http://www.jstor.org/stable/2000275 The fifth and seventh order mock theta functions]. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
 * <cite class="" id="CITEREFAndrews1988" style="line-height: 2em; font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="line-height: 2em;">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
+:<math>f_0(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_{n}}</math>
+:<math>f_1(q) = \sum_{n\ge 0} {q^{n^2+n}\over (-q;q)_{n}}</math>
+:<math>\phi_0(q) = \sum_{n\ge 0} {q^{n^2}(-q;q^2)_{n}}</math>

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-−
-−
 ==related items==
+* [[WRT (Witten-Reshetikhin-Turaev) invariant]]
-−
 ==articles==
 * G.E. Andrews, [http://www.jstor.org/stable/2000275 The fifth and seventh order mock theta functions]. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
-* <cite class="" id="CITEREFAndrews1988" style="line-height: 2em; font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="line-height: 2em;">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>
+* <cite class="" id="CITEREFAndrews1988" style="line-height: 2em; font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="line-height: 2em;">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>
-* [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions]<br>
+* Basil Gordon and Richard J. Mcintosh [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions], 2003
 [[분류:개인노트]]
 [[분류:math and physics]]
 [[분류:mock modular forms]]
 [[분류:math]]

← 이전 판	2020년 11월 16일 (월) 17:49 판
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← 이전 판		2013년 2월 8일 (금) 22:08 판
104번째 줄:		104번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:mock modular forms]]		[[분류:mock modular forms]]
		+	[[분류:math]]

← 이전 판		2012년 11월 2일 (금) 02:47 판
38번째 줄:		38번째 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]]~~	+

@@ 23번째 줄: / 23번째 줄: @@
 * http://ko.wikipedia.org/wiki/
 * http://en.wikipedia.org/wiki/
-* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])