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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • MathSciNet review: 942157