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单词 wpfunction
释义

-function


Let L be a lattice on . The Weierstrass functionMathworldPlanetmath associated to L is given by

(z)=1z2+wL{0}(1(z-w)2-1w2).

The function is meromorphic and analytic on L, whereas at each wL, it has an order 2 pole. It is also an even functionMathworldPlanetmath, because (z)=(-z).

Its derivative

(z)=-2wL1(z-w)3

is also an odd, meromorphic, and elliptic functionMathworldPlanetmath, analytic at L and having order 3 poles at each wL.

The functions and form together a generator set for the field of elliptic functions associated to the lattice L.

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更新时间:2025/5/4 13:22:39