# Functions, Abelian

### From Library of Congress Subject Headings

# Functions, Abelian

### URI(s)

- http://id.loc.gov/authorities/subjects/sh85052329
- info:lc/authorities/sh85052329
- http://id.loc.gov/authorities/sh85052329#concept

### Instance Of

### Scheme Membership(s)

### Collection Membership(s)

### Variants

- Abelian functions
- Abelian integrals
- Hyper-elliptic integrals
- Hyperelliptic functions
- Hyperelliptic integrals
- Integrals, Abelian

### Broader Terms

- Functions of complex variables

### Closely Matching Concepts from Other Schemes

### Sources

- found: Encyc. math. (a generalization of the concept of an elliptic function of one complex variable to the case of several complex variables)
- found: Eric Weisstein's world of mathematics, via WWW, Jan. 27, 2003: Abelian function (an inverse function of an Abelian integral; Abelian functions are a generalization of elliptic functions, and are also called hyperelliptic functions) Abelian integral (also called hyperelliptic integrals)
- found: Encyc. of mathematics on CD-ROM, 1997: hyper-elliptic integral (the special case of an Abelian integral)
- found: The MacTutor history of mathematics archive, via WWW, Jan. 30, 2003: index of glossary terms (Abelian or hyperelliptic function. An abelian or hyperelliptic function is a generalisation of an elliptic function. It is a function of two variables with four periods. In a similar way to an elliptic function it can also be regarded as the inverse function to certain integrals (called Abelian or hyperelliptic integrals) of the form [integral of] dz/[square root of] R(z) where R is a polynomial of degree greater than 4)

### LC Classification

- QA345

### Change Notes

- 2003-01-31: new
- 2003-03-17: revised

### Alternate Formats

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