# Weierstrass form

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## 9 matching pages

##### 1: 31.2 Differential Equations

###### Weierstrass’s Form

…##### 2: 23.21 Physical Applications

##### 3: 29.2 Differential Equations

##### 4: 23.9 Laurent and Other Power Series

##### 5: 23.20 Mathematical Applications

###### §23.20 Mathematical Applications

►###### §23.20(i) Conformal Mappings

… ► … ►###### §23.20(iii) Factorization

… ►###### §23.20(v) Modular Functions and Number Theory

…##### 6: 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 Equation (19.25.35) has been replaced by

in which the left-hand side $z$ has been replaced by $z+2\omega $ for some $2\omega \in \mathbb{L}$, and the right-hand side has been multiplied by $\pm 1$. Equation (19.25.37) has been replaced by

in which the left-hand side $\zeta \left(z\right)+z\mathrm{\wp}\left(z\right)$ has been replaced by $\zeta \left(z+2\omega \right)+(z+2\omega )\mathrm{\wp}\left(z\right)$ and the right-hand side has been multiplied by $\pm 1$. Equation (19.25.39) has been replaced by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 Equation (19.25.40) has been replaced by

in which the left-hand side $z$ has been replaced by $z+2\omega $, and the right-hand side was multiplied by $\pm 1$.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.*

##### 7: Software Index

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23 Weierstrass Elliptic and Modular Functions | |||||||||||||||||||||||||

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These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.