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Abstract: The Extended Engel Expansion is an algorithm that leads to unique series expansions of q-series. Various examples related to classical partition theorems, including the Rogers-Ramanujan identities, have been given recently. The object of this paper is to show that the new and elegant Rogers-Ramanujan generalization found by Garrett, Ismail, and Stanton also fits into this framework. This not only reveals the existence of an infinite, parameterized family of extended Engel expansions, but also... (Update)
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...= 1 q; 1.2) Em = Em Gamma1 q m Em Gamma2 ; E 0 = 1; E 1 = 1: 1. 3) Another proof, based on generalized Engel expansions, can be found in [3]. Schur [8] has computed the limits D1 = 1 Y n=0 1 (1 Gamma q 5n 1 ) 1 Gamma q 5n 4 ) E1 = 1 Y n=0 1 (1 Gamma q 5n 2 ) 1 Gamma q...
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Schur's Determinants and Partition Theorems - Ismail, Prodinger, Stanton (2000) (Correct)
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BibTeX entry: (Update)
G. Andrews, A. Knopfmacher, and P. Paule, An infinite family of Engel expansions of Rogers--Ramanujan type. Adv. Appl. Math., to appear, 2000. http://citeseer.ist.psu.edu/andrews00infinite.html More
@misc{ andrews00infinite,
author = "G. Andrews and A. Knopfmacher and P. Paule",
title = "An infinite family of Engel expansions of Rogers--Ramanujan type",
text = "G. Andrews, A. Knopfmacher, and P. Paule, An infinite family of Engel expansions
of Rogers--Ramanujan type. Adv. Appl. Math., to appear, 2000.",
year = "2000",
url = "citeseer.ist.psu.edu/andrews00infinite.html" }
Citations (may not include all citations):442 Concrete Mathematics (context) - Graham, Knuth et al. - 1994
114 The Theory of Partitions (context) - Andrews
18 Short and easy computer proofs of the Rogers-Ramanujan ident.. - Paule - 1994
11 Inverse polynomials expansions of Laurent series (context) - Knopfmacher, Knopfmacher - 1988
8 Variants of the Rogers-Ramanujan identities - Garrett, Ismail et al. - 1999
8 A polynomial identity which implies the Rogers-Ramanujan ide.. (context) - Andrews - 1970
5 An algorithmic approach to discovering and proving q-series .. - Andrews, Knopfmacher
4 Engel expansions and the RogersRamanujan identities (context) - Andrews, Knopfmacher et al.
3 Ein Beitrag zur additiven Zahlentheorie und zur Theorie der .. (context) - Schur - 1973
1 Irrationalzahlen (context) - Perron - 1951
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On the Largest Degree of an Irreducible Factor of a.. - Knopfmacher.. (1997) (Correct)
Combinatorics of Geometrically Distributed Random.. - Knopfmacher, Prodinger (Correct)
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