Elliptic integrals: Symmetry and symbolic integration

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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 ... continued below

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20 p.

Creation Information

Carlson, B.C. December 31, 1997.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 28 times . More information about this article can be viewed below.

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  • Carlson, B.C. Iowa State Univ., Ames, IA (United States). Dept. of Mathematics

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  • Ames Laboratory
    Publisher Info: Ames Lab., IA (United States)
    Place of Publication: Iowa

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Description

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.

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20 p.

Notes

OSTI as DE99002534

Source

  • Tricomi`s ideas and contemporary applied mathematics, Turin (Italy), 1-2 Dec 1997

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  • Other: DE99002534
  • Report No.: IS-M--876
  • Report No.: CONF-971291--
  • Grant Number: W-7405-ENG-82
  • Office of Scientific & Technical Information Report Number: 348931
  • Archival Resource Key: ark:/67531/metadc680039

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  • December 31, 1997

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • Nov. 6, 2015, 8:58 p.m.

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Carlson, B.C. Elliptic integrals: Symmetry and symbolic integration, article, December 31, 1997; Iowa. (digital.library.unt.edu/ark:/67531/metadc680039/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.