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Title	Elliptic integrals: Symmetry and symbolic integration
Creator/Author	Carlson, B.C. [Ames Lab., IA (United States)]|[Iowa State Univ., Ames, IA (United States). Dept. of Mathematics]
Publication Date	1997 Dec 31
OSTI Identifier	OSTI ID: 348931 ; DE99002534
Report Number(s)	IS-M--876; CONF-971291--
DOE Contract Number	W-7405-ENG-82
Resource Type	Conference
Resource Relation	Tricomi`s ideas and contemporary applied mathematics, Turin (Italy), 1-2 Dec 1997 ; PBD:[1997]
Research Org	Ames Lab., IA (United States)
Sponsoring Org	USDOE Office of Energy Research, Washington, DC (United States)
Subject	99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS ; INTEGRALS; INTEGRAL CALCULUS; ITERATIVE METHODS; ALGORITHMS; FUNCTIONS
Description/Abstract	Computation of elliptic integrals, whether numerical or symbolic, has been aided by the contributions of Italian mathematicians. Tricomi had a strong interest in iterative algorithms for computing elliptic integrals and other special functions, and his writings on elliptic functions and elliptic integrals have taught these subjects to many modern readers (including the author). The theory of elliptic integrals began with Fagnano`s duplication theorem, a generalization of which is now used iteratively for numerical computation in major software libraries. One of Lauricella`s multivariate hypergeometric functions has been found to contain all elliptic integrals as special cases and has led to the introduction of symmetric canonical forms. These forms provide major economies in new integral tables and offer a significant advantage also for symbolic integration of elliptic integrals. Although partly expository the present paper includes some new proofs and proposes a new procedure for symbolic integration.
Country of Publication	United States
Language	English
Format	20 p. ; PL:
Availability	OSTI as DE99002534 To purchase this media from NTIS, click here
System Entry Date	2001 May 04
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