## Experimental Mathematics

### New representations for the Madelung constant

Richard E. Crandall

#### 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.

#### Article information

Source
Experiment. Math. Volume 8, Issue 4 (1999), 367-379.

Dates
First available in Project Euclid: 9 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1047262358

Mathematical Reviews number (MathSciNet)
MR1737232

Zentralblatt MATH identifier
0949.11062

#### Citation

Crandall, Richard E. New representations for the Madelung constant. Experiment. Math. 8 (1999), no. 4, 367--379. http://projecteuclid.org/euclid.em/1047262358.