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

@@ 1번째 줄: / 1번째 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;">introduction</h5>
+==related items==
+* [[manufacturing matrices from lower ranks]]
+* [[q-analogue of summation formulas]]
+* [[Rogers-Ramanujan continued fraction]]
-*   q-Pfaff-Sallschutz sum<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)
-<h5 style="BACKGROUND-POSITION: 0px 100%; FONT-SIZE: 1.16em; MARGIN: 0px; COLOR: rgb(34,61,103); LINE-HEIGHT: 2em; FONT-FAMILY: 'malgun gothic', dotum, gulim, sans-serif;">Bailey lemma</h5>
+* [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.
-If the sequence <math>\{\alpha_r\}, \{\beta_r\}</math>, <math>\{\delta_r\}, \{\gamma_r\}</math> satisfy the following
+* [http://matwbn.icm.edu.pl/ksiazki/aa/aa43/aa4326.pdf Special values of the dilogarithm function]
-<math>\beta_L=\sum_{r=0}^{L}{\alpha_r}{u_{L-r}v_{L+r}}</math>, <math>\gamma_L=\sum_{r=L}^{\infty}{\delta_r}{u_{r-L}v_{r+L}}</math>
-then,
-<math>\sum_{n=0}^{\infty}\alpha_n\gamma_{n}=\sum_{n=0}^{\infty}\beta_n\delta_{n}</math>
-(corollay)
-Choose the following
-<math>u_{n}=\frac{1}{(q)_n}</math> ,<math>v_{n}=\frac{1}{(x)_n}</math>,<math>\delta_n=\frac{(y)_n(z)_n x^n}{y^n z^n}</math>
-Then by the basic analogue of Gauss's theorem ([[#]])
- <math>\gamma_n=\prod{{x/y,x/z;q}\choose {x,x/yz;}}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}</math>
-Hence by Bailey's lemma,
-<math>\sum_{n=0}^{\infty}\frac{(y)_n(z)_n x^n}{y^n z^n}\beta_{n}=\prod{{x/y,x/z;q}\choose {x,x/yz;}}\sum_{n=0}^{\infty}\frac{(y)_n(z)_n x^n}{(x/y)_{n}(x/z)_{n}y^n z^n}\alpha_{n}</math>
-<h5 style="MARGIN: 0px; LINE-HEIGHT: 2em;">Bailey pair</h5>
-*  the sequence <math>\{\alpha_r\}, \{\beta_r\}</math> satisfying the following is called a Bailey pair<br><math>\beta_L=\sum_{r=0}^{L}\frac{\alpha_r}{(q)_{L-r}(aq)_{L+r}}</math><br>
-*  conjugate Bailey pair  <math>\{\delta_r\}, \{\gamma_r\}</math><br><math>\gamma_L=\sum_{r=L}^{\infty}\frac{\delta_r}{(q)_{r-L}(aq)_{r+L}}</math><br>
-<h5 style="MARGIN: 0px; LINE-HEIGHT: 2em;">Bailey chain</h5>
-*  we derive a new Bailey chain from a known Bailey pair<br><math>\alpha^\prime_n= \frac{(\rho_1;q)_n(\rho_2;q)_n(aq/\rho_1\rho_2)^n}{(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\alpha_n</math><br><math>\beta^\prime_n = \sum_{j\ge0}\frac{(\rho_1;q)_j(\rho_2;q)_j(aq/\rho_1\rho_2;q)_{n-j}(aq/\rho_1\rho_2)^j}{(q;q)_{n-j}(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\beta_j</math><br>
-*  corollary. by taking  <math>\rho_1,\rho_2\to \infty</math> , we get <br><math>\alpha^\prime_n= a^nq^{n^2}\alpha_n</math><br><math>\beta^\prime_n = \sum_{r=0}^{L}\frac{a^rq^{r^2}}{(q)_{L-r}}\beta_j</math><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>
-<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;">encyclopedia</h5>
-* http://en.wikipedia.org/wiki/Bailey_pair
-* http://en.wikipedia.org/wiki/Wilfrid_Norman_Bailey
-* http://en.wikipedia.org/wiki/
-* http://www.scholarpedia.org/
-* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
-<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;">books</h5>
-* [[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=
-[[4909919|]]
-<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>
-* [http://arxiv.org/abs/0910.2062v2 50 Years of Bailey's lemma]<br>
-**  S. Ole Warnaar, 2009<br>
-* [http://arxiv.org/abs/math.QA/9909044 A generalization of the q-Saalschutz sum and the Burge transform]<br>
-**  A. Schilling, S.O. Warnaa, 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>
+* [http://dx.doi.org/10.1112%2Fjlms%2Fs1-37.1.504 Wilfrid Norman Bailey]
-**  Slater, L. J. (1962), Journal of the London Mathematical Society. Second Series 37: 504–512<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]<br>
+* [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<br>
+**  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]<br>
+* [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<br>
+**  Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475
-*  On two theorems of combinatory analysis and some allied identities <br>
+* [http://plms.oxfordjournals.org/cgi/reprint/s2-50/1/1.pdf Identities of Rogers-Ramanujan type]
-* http://www.ams.org/mathscinet<br>
+**  Bailey, 1944
+[[분류:math and physics]]
-* http://www.zentralblatt-math.org/zmath/en/
+[[분류:migrate]]
-* http://pythagoras0.springnote.com/
-* http://math.berkeley.edu/~reb/papers/index.html[http://www.ams.org/mathscinet ]
-* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
-* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
-* http://dx.doi.org/10.1112/plms/s2-53.6.460
-<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;">question and answers(Math Overflow)</h5>
-* http://mathoverflow.net/search?q=
-* http://mathoverflow.net/search?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;">blogs</h5>
-*  구글 블로그 검색<br>
-** http://blogsearch.google.com/blogsearch?q=
-** http://blogsearch.google.com/blogsearch?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;">experts on the field</h5>
-* http://arxiv.org/
-<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;">links</h5>
-* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
+==메타데이터==
-* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
+===위키데이터===
-* [http://www.research.att.com/~njas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
+* ID :  [https://www.wikidata.org/wiki/Q4848398 Q4848398]
-* http://functions.wolfram.com/
+===Spacy 패턴 목록===
-*
+* [{'LOWER': 'bailey'}, {'LEMMA': 'pair'}]

"Bailey pair and lemma"의 두 판 사이의 차이

2021년 2월 17일 (수) 02:50 기준 최신판

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