Weierstrass M-test

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21: 19.25 Relations to Other Functions
§19.25(vi) Weierstrass Elliptic Functions
Let $\mathbb{L}$ be a lattice for the Weierstrass elliptic function $\wp\left(z\right)$. …The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which $\wp\left(z\right)-e_{j}<0$, for some $j$. … for some $2\omega_{j}\in\mathbb{L}$ and $\wp\left(\omega_{j}\right)=e_{j}$. … in which $2\omega_{1}$ and $2\omega_{3}$ are generators for the lattice $\mathbb{L}$, $\omega_{2}=-\omega_{1}-\omega_{3}$, and $\eta_{j}=\zeta\left(\omega_{j}\right)$ (see (23.2.12)). …
22: 29.2 Differential Equations
we have
29.2.9 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\eta}^{2}}+(g-\nu(\nu+1)\wp\left(\eta% \right))w=0,$
For the Weierstrass function $\wp$ see §23.2(ii). …
23: 23.22 Methods of Computation
§23.22(ii) Lattice Calculations
The corresponding values of $e_{1}$, $e_{2}$, $e_{3}$ are calculated from (23.6.2)–(23.6.4), then $g_{2}$ and $g_{3}$ are obtained from (23.3.6) and (23.3.7). … Suppose that the invariants $g_{2}=c$, $g_{3}=d$, are given, for example in the differential equation (23.3.10) or via coefficients of an elliptic curve (§23.20(ii)). … Assume $c=g_{2}=-4(3-2i)$ and $d=g_{3}=4(4-2i)$. …
25: 19.10 Relations to Other Functions
§19.10(i) Theta and Elliptic Functions
For relations of Legendre’s integrals to theta functions, Jacobian functions, and Weierstrass functions, see §§20.9(i), 22.15(ii), and 23.6(iv), respectively. …
26: 25.1 Special Notation
The main related functions are the Hurwitz zeta function $\zeta\left(s,a\right)$, the dilogarithm $\mathrm{Li}_{2}\left(z\right)$, the polylogarithm $\mathrm{Li}_{s}\left(z\right)$ (also known as Jonquière’s function $\phi\left(z,s\right)$), Lerch’s transcendent $\Phi\left(z,s,a\right)$, and the Dirichlet $L$-functions $L\left(s,\chi\right)$.
28: 20.9 Relations to Other Functions
§20.9(ii) Elliptic Functions and Modular Functions
See §§22.2 and 23.6(i) for the relations of Jacobian and Weierstrass elliptic functions to theta functions. …
29: Bibliography E
• U. Eckhardt (1980) Algorithm 549: Weierstrass’ elliptic functions. ACM Trans. Math. Software 6 (1), pp. 112–120.
• M. Eichler and D. Zagier (1982) On the zeros of the Weierstrass $\wp$-function. Math. Ann. 258 (4), pp. 399–407.