Finite Rogers-Ramanujan type continued fractions
Keywords:
Bressoud polynomials, Santos polynomials, Rogers–Ramanujan identities
Abstract
New finite continued fractions related to Bressoud and Santos polynomials are established.
References
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G. E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger, q–Engel series expansions and Slater’s identities, Quaest. Math. 24(3) (2001) 403–416.
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.
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D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.
N. S. S. Gu, H. Prodinger, On some continued fraction expansions of the Rogers–Ramanujan type, Ramanujan J. 26(3) (2011) 323–367.
A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.
G. E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger, q–Engel series expansions and Slater’s identities, Quaest. Math. 24(3) (2001) 403–416.
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.
G. E. Andrews, J. P. O. Santos, Rogers–Ramanujan type identities for partitions with attached odd parts, Ramanujan J. 1(1) (1997) 91–99.
B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer–Verlag, New York, 1991.
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.
D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.
N. S. S. Gu, H. Prodinger, On some continued fraction expansions of the Rogers–Ramanujan type, Ramanujan J. 26(3) (2011) 323–367.
A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.
