The zeta-function and the sigma-function of Weierstrass
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).
KeywordsEntire Function Meromorphic Function Elliptic Function Simple Polis Basic Period
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