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I've come across two equivalent definitions of the Weierstrass $\wp$-function, but don't know how to prove that they are equivalent.

Definition 1
$\wp(z)=cf(z)+d$ where $f$ is the elliptic function w.r.t. $\Lambda$ with a pole of order $2$ at $0$ and a zero of order $2$ at $-\frac{1}{2}-\frac{\lambda}{2}$, and $c$, $d$ constants s.t. $c_{-2}=1$, $c_0=0$ in the Laurent expansion of $\wp$ about $0$. In terms of the $\theta$ function $f(z)=e^{2\pi i z}\frac{\theta(z)^2}{\theta(z-\frac{1}{2}-\frac{\lambda}{2})^2}$.

Definition 2
$\wp(z)=\frac{1}{z^2}+\sum_{\lambda\in\Lambda\setminus0}\left(\frac{1}{(z-\lambda)^2}-\frac{1}{\lambda^2}\right)$

Has anyone got a good reference where these are proved to be equivalent, or a nice idea for a quick proof? Many thanks!

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    See markusevich book on theory of functions of a com$p$lex variable PART III chapters 5 and 62013-12-20

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