"Bailey pair and lemma"의 두 판 사이의 차이

2010년 6월 11일 (금) 06:13 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
\(\alpha^\prime_n= \frac{(\rho_1;q)_n(\rho_2;q)_n(aq/\rho_1\rho_2)^n\alpha_n}{(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\)
\(\beta^\prime_n = \sum_{j\ge0}\frac{(\rho_1;q)_j(\rho_2;q)_j(aq/\rho_1\rho_2;q)_{n-j}(aq/\rho_1\rho_2)^j\beta_j}{(q;q)_{n-j}(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\)

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+*   <br>
 * [http://arxiv.org/abs/0910.2062v2 50 Years of Bailey's lemma]<br>
 **  S. Ole Warnaar, 2009<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>
+*   <br>[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5670 Finite Rogers-Ramanujan Type Identities]<br>
-*  Andrew V. Sills, 2003<br>
+**  Andrew V. Sills, 2003<br>
 * [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities]<br>
 **  Mc Laughlin<br>