Elliptic integrals: Symmetry and symbolic integration
- Ames Lab., IA (United States)
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.
- Research Organization:
- Ames Lab., Ames, IA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-82
- OSTI ID:
- 348931
- Report Number(s):
- IS-M-876; CONF-971291-; ON: DE99002534; TRN: AHC29920%%82
- Resource Relation:
- Conference: Tricomi`s ideas and contemporary applied mathematics, Turin (Italy), 1-2 Dec 1997; Other Information: PBD: [1997]
- Country of Publication:
- United States
- Language:
- English
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