Bibliographic Citation | |
Full Text | |
---|---|
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 |
Document Discussions | |
Top |