The zeta-function and the sigma-function of Weierstrass

  • Komaravolu Chandrasekharan
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 281)


Weierstrass’s ζ-function 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).


Entire Function Meromorphic Function Elliptic Function Simple Polis Basic Period 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Komaravolu Chandrasekharan
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichZürichSwitzerland

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