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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Some infinite product identities


Authors: Richard Blecksmith, John Brillhart and Irving Gerst
Journal: Math. Comp. 51 (1988), 301-314
MSC: Primary 05A17; Secondary 05A19, 11P57
MathSciNet review: 942157
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Abstract: In this paper we derive the power series expansions of four infinite products of the form

$\displaystyle \prod\limits_{n \in {S_1}} {(1 - {x^n})\;\prod\limits_{n \in {S_2}} {(1 + {x^n}),} } $

where the index sets $ {S_1}$ and $ {S_2}$ are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1988-0942157-2
PII: S 0025-5718(1988)0942157-2
Keywords: Jacobi triple product, quintuple product, infinite product expansions
Article copyright: © Copyright 1988 American Mathematical Society