Weierstrass form
(0.001 seconds)
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
Originally, the second term on the righthand side was missing. The form of the equation where the second term is missing is correct if the ${}_{2}\varphi _{1}$ is terminating. It is this form which appeared in the first edition of Gasper and Rahman (1990). The more general version which appears now is what is reproduced in Gasper and Rahman (2004, (III.5)).
Reported by Roberto S. CostasSantos on 20190426
Originally, the factor of 2 was missing from the denominator of the argument of the $\mathrm{cot}$ function.
Reported by Blagoje Oblak on 20190527

•
The factor on the righthand side of Equation (10.9.26) containing $\mathrm{cos}(\mu \nu )\theta $ has been been replaced with $\mathrm{cos}\left((\mu \nu )\theta \right)$ to clarify the meaning.

•
In Paragraph Confluent Hypergeometric Functions in §10.16, several Whittaker confluent hypergeometric functions were incorrectly linked to the definitions of the Kummer confluent hypergeometric and parabolic cylinder functions. However, to the eye, the functions appeared correct. The links were corrected.

•
In Equation (15.6.9), it was clarified that $\lambda \in \u2102$.

•
Originally Equation (19.16.9) had the constraint $a,{a}^{\prime}>0$. This constraint was replaced with ${b}_{1}+\mathrm{\cdots}+{b}_{n}>a>0$, ${b}_{j}\in \mathbb{R}$. It therefore follows from Equation (19.16.10) that ${a}^{\prime}>0$. The last sentence of Subsection 19.16(ii) was elaborated to mention that generalizations may also be found in Carlson (1977b). These were suggested by Bastien Roucariès.

•
In Section 19.25(vi), the Weierstrass lattice roots ${e}_{j},$ were labeled 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)). This was reported by Felix Ospald.

•
In Equation (19.25.37), 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.

•
In Equation (27.12.5), the term originally written as $\sqrt{\mathrm{ln}x}$ was rewritten as ${(\mathrm{ln}x)}^{1/2}$ to be consistent with other equations in the same subsection.
Originally the denominator ${(zw)}^{2}$ was given incorrectly as $(z{w}^{2})$.
Reported 20120216 by James D. Walker.
Originally the limiting form for $\mathrm{sc}(z,k)$ in the last line of this table was incorrect ($\mathrm{cosh}z$, instead of $\mathrm{sinh}z$).
$\mathrm{sn}(z,k)$ $\to $  $\mathrm{tanh}z$  $\mathrm{cd}(z,k)$ $\to $  $1$  $\mathrm{dc}(z,k)$ $\to $  $1$  $\mathrm{ns}(z,k)$ $\to $  $\mathrm{coth}z$ 

$\mathrm{cn}(z,k)$ $\to $  $\mathrm{sech}z$  $\mathrm{sd}(z,k)$ $\to $  $\mathrm{sinh}z$  $\mathrm{nc}(z,k)$ $\to $  $\mathrm{cosh}z$  $\mathrm{ds}(z,k)$ $\to $  $\mathrm{csch}z$ 
$\mathrm{dn}(z,k)$ $\to $  $\mathrm{sech}z$  $\mathrm{nd}(z,k)$ $\to $  $\mathrm{cosh}z$  $\mathrm{sc}(z,k)$ $\to $  $\mathrm{sinh}z$  $\mathrm{cs}(z,k)$ $\to $  $\mathrm{csch}z$ 
Reported 20101123.
7: Software Index
Open Source  With Book  Commercial  

…  
23 Weierstrass Elliptic and Modular Functions  
… 
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.