Asymptotic formulas for elliptic integrals

dc.contributor.author Gustafson, John
dc.contributor.department Mathematics
dc.date 2018-08-15T13:36:27.000
dc.date.accessioned 2020-07-02T06:00:54Z
dc.date.available 2020-07-02T06:00:54Z
dc.date.copyright Fri Jan 01 00:00:00 UTC 1982
dc.date.issued 1982
dc.description.abstract <p>Asymptotic formulas are derived for incomplete elliptic integrals of all three kinds when the arguments are real and tend to infinity or to zero. Practical error bounds are found for the asymptotic formulas. Several techniques are used, including a method recently discovered by R. Wong for finding asymptotic expansions with remainder terms for integral transforms. Most of the asymptotic formulas and all of the error bounds appear to be new;We use incomplete elliptic integrals which possess a high degree of permutation symmetry in the function arguments. The asymptotic formulas are applicable to complete elliptic integrals as a special case; some of the error bounds are treated separately in the complete case;Numerical examples are given to demonstrate the typicalaccuracy which can be expected from the formulas, as well as the;closeness of the error bounds;*DOE Report IS-T-1014. This work was performed under ContractNo. W-7405-Eng-82 with the U.S. Department of Energy.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/7501/
dc.identifier.articleid 8500
dc.identifier.contextkey 6314475
dc.identifier.doi https://doi.org/10.31274/rtd-180813-5069
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/7501
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/80386
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/7501/r_8224219.pdf|||Sat Jan 15 01:49:38 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics
dc.title Asymptotic formulas for elliptic integrals
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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