On series expansions of Capparelli's infinite product
نویسندگان
چکیده
منابع مشابه
On Series Expansions of Capparelli’s Infinite Product
Using Lie theory, Stefano Capparelli conjectured an interesting Rogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using combinatorial methods. Later, Capparelli was able to provide a Lie theoretic proof. Most combinatorial Rogers-Ramanujan type identities (e.g. the Göllnitz-Gordon identities, Gordon’s combinatorial generaliza...
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We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if (qr−tk, qmk−(r−tk); q)∞ (qr, qmk−r; q)∞ =: ∞ ∑ n=0 cnq , for certain integers k, m s and t, where r = sm+t, then ckn−rs is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also...
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W. T. Sulaiman Department of Mathematic, College of Computer Science and Mathematics, Mosul University, Mosul, Iraq Correspondence should be addressed to W. T. Sulaiman, [email protected] Received 14 October 2007; Accepted 21 April 2008 Recommended by Huseyin Bor New results concerning product summability of an infinite series are given. Some special cases are also deduced. Copyright q 2...
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In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...
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In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2004
ISSN: 0196-8858
DOI: 10.1016/j.aam.2003.09.005