Weierstrass elliptic-function form

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31: William P. Reinhardt

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23 Weierstrass Elliptic and Modular Functions

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32: 20.9 Relations to Other Functions

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§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. …

33: Software Index

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	Open Source													With Book						Commercial
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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.

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34: Bibliography E

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Algorithm 549: Weierstrass’ elliptic functions. ACM Trans. Math. Software 6 (1), pp. 112–120.

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Notes:

Single-precision Fortran, maximum accuracy 18D.

External Links:

ISSN 0098-3500, Document, GAMS (module 549; package TOMS)

Referenced by:

1st item.

Encodings:

BibTeX

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On the zeros of the Weierstrass $\mathrm{\wp }$-function. Math. Ann. 258 (4), pp. 399–407.

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External Links:

ISSN 0025-5831, Document, MathReview (Toyokazu Hiramatsu), ZentralBlatt

Referenced by:

§23.13.

Encodings:

BibTeX

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35: 33.18 Limiting Forms for Large $\mathrm{\ell }$

§33.18 Limiting Forms for Large $\mathrm{\ell }$

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36: 1.9 Calculus of a Complex Variable

… ►or in polar form (1.9.3) $u$ and $v$ satisfy … ►or its limiting form, and is invariant under bilinear transformations. … ►

Weierstrass $M$-test

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37: 31.12 Confluent Forms of Heun’s Equation

§31.12 Confluent Forms of Heun’s Equation

►Confluent forms of Heun’s differential equation (31.2.1) arise when two or more of the regular singularities merge to form an irregular singularity. …There are four standard forms, as follows: … ►This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\mathrm{\infty }$. … ►

38: 22.1 Special Notation

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39: 32.13 Reductions of Partial Differential Equations

… ►Depending whether $A=0$ or $A\ne 0$, $v(z)$ is expressible in terms of the Weierstrass elliptic function (§23.2) or solutions of ${\text{P}}_{\text{I}}$, respectively. …

40: Frank Garvan

… ►His research is in the areas of $q$-series and modular forms, and he enjoys using MAPLE in his research. …