Finite Rogers-Ramanujan type continued fractions

Öz

New finite continued fractions related to Bressoud and Santos polynomials are established.

Anahtar Kelimeler

• Bressoud polynomials,Santos polynomials,Rogers–Ramanujan identities

Kaynakça

1. [1] G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison–Wesley Publishing Co., Reading, Mass.–London–Amsterdam, 1976.
2. [2] G. E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger, q–Engel series expansions and Slater’s identities, Quaest. Math. 24(3) (2001) 403–416.
3. [3] G. E. Andrews, A. Knopfmacher, P. Paule, An infinite family of Engel expansions of Rogers– Ramanujan type, Adv. Appl. Math. 25(1) (2000) 2–11.
4. [4] G. E. Andrews, J. P. O. Santos, Rogers–Ramanujan type identities for partitions with attached odd parts, Ramanujan J. 1(1) (1997) 91–99.
5. [5] B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer–Verlag, New York, 1991.
6. [6] B. C. Berndt, S. S. Huang, J. Sohn, S. H. Son, Some theorems on the Rogers–Ramanujan continued fraction in Ramanujan’s lost notebook, Trans. Amer. Math. Soc. 352 (2000) 2157–2177.
7. [7] D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
8. [8] R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.

9. [9] N. S. S. Gu, H. Prodinger, On some continued fraction expansions of the Rogers–Ramanujan type, Ramanujan J. 26(3) (2011) 323–367.
10. [10] A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
11. [11] L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.