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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Some infinite product identities
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by Richard Blecksmith, John Brillhart and Irving Gerst PDF
Math. Comp. 51 (1988), 301-314 Request permission

Abstract:

In this paper we derive the power series expansions of four infinite products of the form \[ \prod \limits _{n \in {S_1}} {(1 - {x^n})\;\prod \limits _{n \in {S_2}} {(1 + {x^n}),} } \] 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
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 301-314
  • MSC: Primary 05A17; Secondary 05A19, 11P57
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942157-2
  • MathSciNet review: 942157