# Weierstrass M-test

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## 31—36 of 36 matching pages

##### 31: Errata

This subsection has been significantly updated. In particular, the following formulae have been corrected. Equation (19.25.35) has been replaced by

in which the left-hand side $z$ has been replaced by $z+2\omega $ for some $2\omega \in \mathbb{L}$, and the right-hand side has been multiplied by $\pm 1$. Equation (19.25.37) has been replaced by

in which the left-hand side $\zeta \left(z\right)+z\mathrm{\wp}\left(z\right)$ has been replaced by $\zeta \left(z+2\omega \right)+(z+2\omega )\mathrm{\wp}\left(z\right)$ and the right-hand side has been multiplied by $\pm 1$. Equation (19.25.39) has been replaced by

in which the left-hand side ${\eta}_{j}$ was replaced by $\zeta \left({\omega}_{j}\right)$, for some $2{\omega}_{j}\in \mathbb{L}$ and $\mathrm{\wp}\left({\omega}_{j}\right)={e}_{j}$. Equation (19.25.40) has been replaced by

in which the left-hand side $z$ has been replaced by $z+2\omega $, and the right-hand side was multiplied by $\pm 1$. For more details see §19.25(vi).

Originally, the factor of 2 was missing from the denominator of the argument of the $\mathrm{cot}$ function.

*Reported by Blagoje Oblak on 2019-05-27*

The Weierstrass lattice roots ${e}_{j},$ were linked inadvertently as the base of the natural logarithm. In order to resolve this inconsistency, the lattice roots ${e}_{j}$, and lattice invariants ${g}_{2}$, ${g}_{3}$, now link to their respective definitions (see §§23.2(i), 23.3(i)).

*Reported by Felix Ospald.*

The Weierstrass zeta function was incorrectly linked to the definition of the Riemann zeta function. However, to the eye, the function appeared correct. The link was corrected.

Originally the denominator ${(z-w)}^{2}$ was given incorrectly as $(z-{w}^{2})$.

*Reported 2012-02-16 by James D. Walker.*