Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions

Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions

Show other versions (1)
Bibliographic Details
Main Author: Conrad, Eric van Fossen
Language:English
Published: The Ohio State University / OhioLINK 2002
Subjects:
Mathematics
Jacobi elliptic functions
Dixon elliptic functions
Hankel determinants
Turanian determinants
persymmetric determinants
associated continued fractions
regular C-fractions
Laplace transform
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1029248229
id ndltd-OhioLink-oai-etd.ohiolink.edu-osu1029248229
record_format oai_dc
spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu10292482292021-08-03T05:47:34Z Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions Conrad, Eric van Fossen Mathematics Jacobi elliptic functions Dixon elliptic functions Hankel determinants Turanian determinants persymmetric determinants associated continued fractions regular C-fractions Laplace transform In a 1907 paper, L. Rogers used two methods to obtain continued fractions for certain Laplace transforms of Jacobi elliptic functions. His first method employed repeated integration by parts, while his second method recalled an 1889 technique of T. Stieltjes. In 1996, S. Milne used these expansions and others obtained by modular transformations to derive results about sums of squares and triangular numbers. Working independently in the 1820's, C. Jacobi and N. Abel both introduced elliptic functions to advance the study of elliptic integrals. In 1981, D. Dumont introduced symmetric variants of the elliptic functions of Jacobi and Abel to facilitate the study of certain combinatorial problems related to coefficients in Maclaurin expansions of Jacobi elliptic functions. In this thesis, we use Dumont's elliptic functions to rederive the ontinued fraction expansions of Rogers. In the classical approach used by Rogers and Milne, four families of continued fractions are obtained. In our approach, members of the same four families are derived directly by pecializing parameters instead of employing modular transformations. To these four families, we add a new set of continued fractions based on certain elliptic functions that were studied in an 1890 paper by A. Dixon. These new continued fractions were discovered in 1999 in the course of work with D. Dumont. 2002-09-11 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1029248229 http://rave.ohiolink.edu/etdc/view?acc_num=osu1029248229 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Jacobi elliptic functions
Dixon elliptic functions
Hankel determinants
Turanian determinants
persymmetric determinants
associated continued fractions
regular C-fractions
Laplace transform
spellingShingle Mathematics
Jacobi elliptic functions
Dixon elliptic functions
Hankel determinants
Turanian determinants
persymmetric determinants
associated continued fractions
regular C-fractions
Laplace transform
Conrad, Eric van Fossen
Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
author Conrad, Eric van Fossen
author_facet Conrad, Eric van Fossen
author_sort Conrad, Eric van Fossen
title Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
title_short Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
title_full Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
title_fullStr Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
title_full_unstemmed Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions
title_sort some continued fraction expansions of laplace transforms of elliptic functions
publisher The Ohio State University / OhioLINK
publishDate 2002
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1029248229
work_keys_str_mv AT conradericvanfossen somecontinuedfractionexpansionsoflaplacetransformsofellipticfunctions
_version_ 1719425359617720320

Similar Items