Bailey pair and lemma
http://bomber0.myid.net/ (토론)님의 2011년 11월 12일 (토) 06:44 판
examples of Bailey pair
- If we apply Bailey lemma to the above conjugate pair, we get
examples
- Conjugate Bailey pair (\(x=q,y\to\infty, z\to\infty\))
\(\delta_n=q^{n^2}\)
\(\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}\) - Bailey pair
\(\alpha_{n}=(-1)^{n}q^{\frac{3}{2}n^2}(q^{\frac{1}{2}n}+q^{-\frac{1}{2}n})\)
\(\beta_n=\frac{1}{(q)_{n}}\) - we get the Rogers-Ramanujan identity(Slater 18)
\(\sum_{n=0}^{\infty}\frac{q^{n^2}}{ (q)_{n}}=\frac{(q^{3};q^{5})_{\infty}(q^{2};q^{5})_{\infty}(q^{5};q^{5})_{\infty}}{(q)_{\infty}}=\frac{1}{(q^{1};q^{5})_{\infty}(q^{4};q^{5})_{\infty}}\)
Bailey chain
history
- Bloch group
- Bloch group, K-theory and dilogarithm
- manufacturing matrices from lower ranks
- q-analogue of summation formulas
- Rogers-Ramanujan continued fraction
articles
-
A. Schilling, S.O. Warnaar A generalization of the q-Saalschutz sum and the Burge transform, 2009 - Rogers-Ramanujan-Slater Type identities
- Mc Laughlin, 2008
- Mc Laughlin, 2008
- Andrews–Gordon type identities from combinations of Virasoro characters
- Boris Feigin, Omar Foda, Trevor Welsh, 2007
- Boris Feigin, Omar Foda, Trevor Welsh, 2007
- Finite Rogers-Ramanujan Type Identities
- Andrew V. Sills, 2003
- 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)
- 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.
- 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
- 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
- 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
- Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475
- Identities of Rogers-Ramanujan type
- Bailey, 1944
- Bailey, 1944