"Bailey pair and lemma"의 두 판 사이의 차이

2010년 6월 18일 (금) 15:15 판

the sequence \(\{\alpha_r\}, \{\beta_r\}\) satisfying the following is called a Bailey pair
\(\beta_L=\sum_{r=0}^{L}\frac{\alpha_r}{(q)_{L-r}(aq)_{L+r}}\)
conjugate Bailey pair \(\{\delta_r\}, \{\gamma_r\}\)
\(\gamma_L=\sum_{r=L}^{\infty}\frac{\delta_r}{(q)_{r-L}(aq)_{r+L}}\)

we derive a new Bailey chain from a known Bailey pair
\(\alpha^\prime_n= \frac{(\rho_1;q)_n(\rho_2;q)_n(aq/\rho_1\rho_2)^n}{(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\alpha_n\)
\(\beta^\prime_n = \sum_{j\ge0}\frac{(\rho_1;q)_j(\rho_2;q)_j(aq/\rho_1\rho_2;q)_{n-j}(aq/\rho_1\rho_2)^j}{(q;q)_{n-j}(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\beta_j\)
corollary. by taking \(\rho_1,\rho_2\to \infty\) , we get

\(\alpha^\prime_n= a^nq^{n^2}\alpha_n\)
\(\beta^\prime_n = \sum_{r=0}^{L}\frac{a^rq^{r^2}}{(q)_{L-r}}\beta_j\)

[[4909919|]]

50 Years of Bailey's lemma
- S. Ole Warnaar, 2009
A generalization of the q-Saalschutz sum and the Burge transform
- A. Schilling, S.O. Warnaa, 2009
Rogers-Ramanujan-Slater Type identities
- Mc Laughlin, 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)
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

@@ 55번째 줄: / 55번째 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;">encyclopedia</h5>
-*   <br>
 * http://en.wikipedia.org/wiki/Bailey_pair
 * http://en.wikipedia.org/wiki/Wilfrid_Norman_Bailey
@@ 85번째 줄: / 84번째 줄: @@
 * [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://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5670 Finite Rogers-Ramanujan Type Identities]<br>
+* [http://www.combinatorics.org/Volume_10/PDF/v10i1r13.pdf Finite Rogers-Ramanujan Type Identities]<br>
 **  Andrew V. Sills, 2003<br>
-* [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities]<br>
-**  Mc Laughlin<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>