"Bailey pair and lemma"의 두 판 사이의 차이

2021년 2월 17일 (수) 02:50 기준 최신판

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articles

Patkowski, Alexander E. ‘A Note on Some Partitions Related to Ternary Quadratic Forms’. arXiv:1503.08516 [math], 29 March 2015. http://arxiv.org/abs/1503.08516.
A. Schilling, S.O. Warnaar A generalization of the q-Saalschutz sum and the Burge transform, 2009
Mc Laughlin Rogers-Ramanujan-Slater Type identities, 2008
Andrews–Gordon type identities from combinations of Virasoro characters
- Boris Feigin, Omar Foda, Trevor Welsh, 2007
Finite Rogers-Ramanujan Type Identities
- Andrew V. Sills, 2003
Virasoro character identities from the Andrews–Bailey construction
- Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)

Multiple series Rogers-Ramanujan type identities.
- George E. Andrews, Pacific J. Math. Volume 114, Number 2 (1984), 267-283.
Special values of the dilogarithm function
- J. H. Loxton, 1984
Wilfrid Norman Bailey
- Slater, L. J. (1962), Journal of the London Mathematical Society. Second Series 37: 504–512
Further identities of the Rogers-Ramanujan type
- Slater, L. J. (1952), Proceedings of the London Mathematical Society. Second Series 54: 147–167
A New Proof of Rogers's Transformations of Infinite Series
- Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475
Identities of Rogers-Ramanujan type
- Bailey, 1944

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ID : Q4848398

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[{'LOWER': 'bailey'}, {'LEMMA': 'pair'}]

@@ 1번째 줄: / 1번째 줄: @@
-<h5 style="margin: 0px; line-height: 2em;">examples of Bailey pair</h5>
+==related items==
+* [[manufacturing matrices from lower ranks]]
+* [[q-analogue of summation formulas]]
+* [[Rogers-Ramanujan continued fraction]]
-* [[Slater list|Slater's list]]<br>
+==articles==
+* Patkowski, Alexander E. ‘A Note on Some Partitions Related to Ternary Quadratic Forms’. arXiv:1503.08516 [math], 29 March 2015. http://arxiv.org/abs/1503.08516.
+*  A. Schilling, S.O. Warnaar [http://arxiv.org/abs/math.QA/9909044 A generalization of the q-Saalschutz sum and the Burge transform], 2009
+* Mc Laughlin [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities], 2008
+* [http://www.springerlink.com/content/478544t414l26v05/ Andrews–Gordon type identities from combinations of Virasoro characters]
+**  Boris Feigin, Omar Foda, Trevor Welsh, 2007
+* [http://www.combinatorics.org/Volume_10/PDF/v10i1r13.pdf Finite Rogers-Ramanujan Type Identities]
+**  Andrew V. Sills, 2003
+* [http://dx.doi.org/10.1142/S0217751X97001110 Virasoro character identities from the Andrews–Bailey construction]
+**  Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)
+* [http://projecteuclid.org/euclid.pjm/1102708707 Multiple series Rogers-Ramanujan type identities.]
+** George E. Andrews, Pacific J. Math.  Volume 114, Number 2 (1984), 267-283.
-<h5 style="margin: 0px; line-height: 2em;">specialization</h5>
+* [http://matwbn.icm.edu.pl/ksiazki/aa/aa43/aa4326.pdf Special values of the dilogarithm function]
+** J. H. Loxton, 1984
-*  Choose the following (in the following, x=aq to get a Bailey pair relative to a)<br><math>u_{n}=\frac{1}{(q)_n}</math> ,<math>v_{n}=\frac{1}{(x)_n}</math>,<br>
+* [http://dx.doi.org/10.1112%2Fjlms%2Fs1-37.1.504 Wilfrid Norman Bailey]
-*  There is a conjugate Bailey pair<br><math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math><br>  <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>
+**  Slater, L. J. (1962), Journal of the London Mathematical Society. Second Series 37: 504–512
+* [http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]
+**  Slater, L. J. (1952),  Proceedings of the London Mathematical Society. Second Series 54: 147–167
+* [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]
+**  Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475
+* [http://plms.oxfordjournals.org/cgi/reprint/s2-50/1/1.pdf Identities of Rogers-Ramanujan type]
-*  If we apply Bailey lemma to the above conjugate pair, we get<br><math>\sum_{n=0}^{\infty}\frac{(y)_n(z)_n x^n}{y^n z^n}\beta_{n}=\frac{(x/y;q)_{\infty}(x/z;q)_{\infty}}{(x;q)_{\infty}(x/yz;q)_{\infty}}}\sum_{n=0}^{\infty}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}\alpha_{n}</math><br>
+**  Bailey, 1944
+[[분류:math and physics]]
+[[분류:migrate]]
-<h5 style="margin: 0px; line-height: 2em;">examples</h5>
-*  Conjugate Bailey pair (<math>x=q,y\to\infty, z\to\infty</math>)<br><math>\delta_n=q^{n^2}</math><br><math>\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}</math><br>
-*  Bailey pair<br><math>\alpha_{n}=(-1)^{n}q^{\frac{3}{2}n^2}(q^{\frac{1}{2}n}+q^{-\frac{1}{2}n})</math><br><math>\beta_n=\frac{1}{(q)_{n}}</math><br>
-*  we get the Rogers-Ramanujan identity([[5974537|Slater 18]])<br><math>\sum_{n=0}^{\infty}\frac{q^{n^2}}{ (q)_{n}}=\frac{(q^{3};q^{5})_{\infty}(q^{2};q^{5})_{\infty}(q^{5};q^{5})_{\infty}}{(q)_{\infty}}=\frac{1}{(q^{1};q^{5})_{\infty}(q^{4};q^{5})_{\infty}}</math><br>
+==메타데이터==
+===위키데이터===
+* ID :  [https://www.wikidata.org/wiki/Q4848398 Q4848398]
+===Spacy 패턴 목록===
-<h5 style="margin: 0px; line-height: 2em;">Bailey chain</h5>
+* [{'LOWER': 'bailey'}, {'LEMMA': 'pair'}]
-* [[6080259|Bailey chain]]<br>
-<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;">history</h5>
-* http://www.google.com/search?hl=en&tbs=tl:1&q=
-<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;">related items</h5>
-* [[Bloch group]]<br>
-* [[Bloch group, K-theory and dilogarithm]]<br>
-* [[1 manufacturing matrices from lower ranks|manufacturing matrices from lower ranks]]<br>
-* [[q-analogue of summation formulas]]<br>
-* [[Rogers-Ramanujan continued fraction]]<br>
-<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;">articles</h5>
-*   <br> A. Schilling, S.O. Warnaar [http://arxiv.org/abs/math.QA/9909044 A generalization of the q-Saalschutz sum and the Burge transform], 2009<br>
-* [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities]<br>
-**  Mc Laughlin, 2008<br>
-* [http://www.springerlink.com/content/478544t414l26v05/ Andrews–Gordon type identities from combinations of Virasoro characters]<br>
-**  Boris Feigin, Omar Foda, Trevor Welsh, 2007<br>
-* [http://www.combinatorics.org/Volume_10/PDF/v10i1r13.pdf Finite Rogers-Ramanujan Type Identities]<br>
-**  Andrew V. Sills, 2003<br>
-* [http://dx.doi.org/10.1142/S0217751X97001110 Virasoro character identities from the Andrews–Bailey construction]<br>
-**  Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)<br>
-* [http://projecteuclid.org/euclid.pjm/1102708707 Multiple series Rogers-Ramanujan type identities.]<br>
-** George E. Andrews, Pacific J. Math.  Volume 114, Number 2 (1984), 267-283.<br>
-* [http://matwbn.icm.edu.pl/ksiazki/aa/aa43/aa4326.pdf Special values of the dilogarithm function]<br>
-** J. H. Loxton, 1984
-* [http://dx.doi.org/10.1112%2Fjlms%2Fs1-37.1.504 Wilfrid Norman Bailey]<br>
-**  Slater, L. J. (1962), Journal of the London Mathematical Society. Second Series 37: 504–512<br>
-* [http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]<br>
-**  Slater, L. J. (1952),  Proceedings of the London Mathematical Society. Second Series 54: 147–167<br>
-* [http://dx.doi.org/10.1112/plms/s2-53.6.460 A New Proof of Rogers's Transformations of Infinite Series]<br>
-**  Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475<br>
-* [http://plms.oxfordjournals.org/cgi/reprint/s2-50/1/1.pdf Identities of Rogers-Ramanujan type]<br>
-**  Bailey, 1944<br>

"Bailey pair and lemma"의 두 판 사이의 차이

2021년 2월 17일 (수) 02:50 기준 최신판

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