Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1148.33017
Dienstfrey, Andrew; Huang, Jingfang
Integral representations for elliptic functions. (English)
[J] J. Math. Anal. Appl. 316, No. 1, 142-160 (2006). ISSN 0022-247X

Summary: We derive new integral representations for constituents of the classical theory of elliptic functions: the Eisenstein series, and Weierstrass' $\wp$ and $\zeta$ functions. The derivations proceed from the Laplace-Mellin representation of multipoles, and an elementary lemma on the summation of 2D geometric series. In addition, we present results concerning the analytic continuation of the Eisenstein series to an entire function in the complex plane, and the value of the conditionally convergent series, denoted by $\widetilde E_2$ below, as a function of summation over increasingly large rectangles with arbitrary fixed aspect ratio.

MSC 2000:: *33E05 Elliptic functions and integrals

Keywords: elliptic functions; Eisenstein series; plane wave expansions; lattice sums

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]