A nested sum over two variables. Identities involving double sums include the following:

(1) |

(2) |

(3) |

Consider the sum

(4) |

(5) | |||

(6) | |||

(7) |

can also be defined, which gives rise to such impressive Formulas as

(8) |

**References**

Glasser, M. L. and Zucker, I. J. ``Lattice Sums in Theoretical Chemistry.'' *Theoretical Chemistry: Advances and Perspectives, Vol. 5.*
New York: Academic Press, 1980.

Zucker, I. J. and Robertson, M. M. ``A Systematic Approach to the Evaluation of
.'' *J. Phys. A: Math. Gen.* **9**, 1215-1225, 1976.

© 1996-9

1999-05-24