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The evaluation of two-dimensional lattice sums via Ramanujan's theta functions

Ping Xu (2014)

Acta Arithmetica

We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.

The Legendre Formula in Clifford Analysis

Laville, Guy, Ramadanoff, Ivan (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.

The new properties of the theta functions

Stefan Czekalski (2013)

Annales mathématiques Blaise Pascal

It is shown, that the function H ( x ) = k = - e - k 2 x satisfies the relation H ( x ) = n = 0 ( 2 π ) 2 n ( 2 n ) ! H ( n ) ( x ) .

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