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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 Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.

Van Fossen Conrad, Eric, Flajolet, Philippe (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

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 Many Limits of Mixed Means. II. The Carlson Sequences.

John Todd (1989)

Numerische Mathematik

The new properties of the theta functions

Stefan Czekalski (2013)

Annales mathématiques Blaise Pascal

It is shown, that the function $\begin{matrix} H (x) & = \sum_{k = - \infty}^{\infty} e^{- k^{2} x} \\ satisfies the relation \\ H (x) & = \sum_{n = 0}^{\infty} \frac{{(2 π)}^{2 n}}{(2 n)!} H^{(n)} (x) . \end{matrix}$

Theorie der elliptischen Functionen [Book]

Heinrich Durège (1878)

Théorie des fonctions elliptiques [Book]

C. A. A. Briot, J. C. Bouquet (1875)

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Techniques of the differential subordination for domains bounded by conic sections.

Teorie eliptických funkcí u Weierstrasse

The addition formula for theta functions.

The addition theorem of Weierstrass' s sigma function.

The algebraic independence of Weierstrass functions and some related numbers

The complete ellipsoidal shell-model in EEG imaging.

The critical values of certain Dirichlet series.

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

The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.

The Legendre Formula in Clifford Analysis

The Many Limits of Mixed Means. II. The Carlson Sequences.

The new properties of the theta functions

The number of representations by sums of squares and triangular numbers.

The Spectrum of Hill's Equation.

The transcendence of certain quasi-periods associated with abelian functions in two variables

Theorie der elliptischen Functionen [Book]

Théorie des fonctions elliptiques [Book]

Théorie élémentaire des fonctions elliptiques

Théorie élémentaire des fonctions elliptiques

Théorie élémentaire des fonctions elliptiques

Currently displaying 1 – 20 of 23