Finite Rogers-Ramanujan type continued fractions

Year 2018, Volume: 5 Issue: 3, 137 - 142, 08.10.2018

Helmut Prodinger

https://doi.org/10.13069/jacodesmath.451218

Abstract

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

Keywords

Bressoud polynomials, Santos polynomials, Rogers–Ramanujan identities

References

• [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] 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] 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] 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] B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer–Verlag, New York, 1991.
• [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] D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
• [8] R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.
• [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] A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
• [11] L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.