Elliptic and Abelian Integrals

Raymond O. Wells ()
Additional contact information
Raymond O. Wells: University of Colorado Boulder

Chapter Chapter 7 in Differential and Complex Geometry: Origins, Abstractions and Embeddings, 2017, pp 83-95 from Springer

Abstract: Abstract With the innovations of calculus, it was discovered that standard trigonometric functions could be formulated as integrals of algebraic function of degree two. Euler and others generalized these to elliptic integrals, integrals of algebraic functions of degree three and four, and Abel generalized these, in turn, to integrals of algebraic functions of arbitrary degree (Abelian integrals). These transcendental functions were multivalued and various generalizations of the classical trigonometric addition formulas were formulated and proved for this more general class of functions.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-58184-2_7

Ordering information: This item can be ordered from
http://www.springer.com/9783319581842

DOI: 10.1007/978-3-319-58184-2_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().