The quantities obtained from cubic, hexagonal, etc., Lattice Sums, evaluated at , are called
Madelung constants. For cubic Lattice Sums, they are expressible in closed form for Even indices,

(1) | |||

(2) |

is given by Benson's Formula,

(3) |

For hexagonal Lattice Sum, is expressible in closed form as

(4) |

**References**

Borwein, J. M. and Borwein, P. B. *Pi & the AGM: A Study in Analytic Number Theory and Computational
Complexity.* New York: Wiley, 1987.

Buhler, J. and Wagon, S. ``Secrets of the Madelung Constant.'' *Mathematica in Education and Research* **5**, 49-55, Spring 1996.

Crandall, R. E. and Buhler, J. P. ``Elementary Function Expansions for
Madelung Constants.'' *J. Phys. Ser. A: Math. and Gen.* **20**, 5497-5510, 1987.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/mdlung/mdlung.html

© 1996-9

1999-05-26