Abstract
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).
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© 1985 Springer-Verlag Berlin Heidelberg
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Chandrasekharan, K. (1985). The zeta-function and the sigma-function of Weierstrass. In: Elliptic Functions. Grundlehren der mathematischen Wissenschaften, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52244-4_4
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DOI: https://doi.org/10.1007/978-3-642-52244-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-52246-8
Online ISBN: 978-3-642-52244-4
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