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1999 New representations for the Madelung constant
Richard E. Crandall
Experiment. Math. 8(4): 367-379 (1999).

Abstract

From a modern theta-function identity of G. E. Andrews we derive new representations for the celebrated Madelung constant and various of its analytic relatives. The method leads to connections with the modern theory of multiple zeta sums, generates an apparently entire "$\eta$ series" representation, and, for the Madelung constant in particular, yields a finite-integral representation. These analyses suggest variants of the Andrews identity, leading in turn to number-theoretical results concerning sums of three squares.

Citation

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Richard E. Crandall. "New representations for the Madelung constant." Experiment. Math. 8 (4) 367 - 379, 1999.

Information

Published: 1999
First available in Project Euclid: 9 March 2003

zbMATH: 0949.11062
MathSciNet: MR1737232

Subjects:
Primary: 11Y60
Secondary: 11E45, 11M35, 33E20, 33F05

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 4 • 1999
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