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The zetafunction and the sigmafunction of Weierstrass

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Chapter

Elliptic Functions

Volume 281 of the series Grundlehren der mathematischen Wissenschaften pp 48­57

The zeta­function and the sigma­function of Weierstrass

Komaravolu Chandrasekharan

Abstract

Weierstrass’s ζ­function is a meromorphic function, which has simple poles, with residues equal to one, at all points which correspond to the periods of Weierstrass’s ℘­function. It is not elliptic. But every elliptic function can be expressed in terms of ζ and its derivatives; in fact ζ(z)= ­℘(z).

About this Chapter

Title

The zeta­function and the sigma­function of Weierstrass Book Title

Elliptic Functions Pages

pp 48­57 Copyright

1985 DOI

10.1007/978­3­642­52244­4_4 Print ISBN

978­3­642­52246­8 Online ISBN

978­3­642­52244­4 Series Title

Grundlehren der mathematischen Wissenschaften Series Volume

281

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Series Subtitle

A Series of Comprehensive Studies in Mathematics Series ISSN

0072­7830 Publisher

Springer Berlin Heidelberg Copyright Holder

Springer­Verlag Berlin Heidelberg Additional Links

About this Book

Topics

Number Theory Special Functions

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Springer Book Archive

Authors

Komaravolu Chandrasekharan (2)

Author Affiliations

2. Eidgenössische Technische Hochschule Zürich, CH­8092, Zürich, Switzerland We use cookies to improve your experience with our site. More information  Accept

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