On Euler's differential methods for continued fractions
| dc.contributor.author | Khrushchev, Sergey | |
| dc.contributor.other | Mathematics | |
| dc.date.accessioned | 2024-10-06T10:57:32Z | |
| dc.date.available | 2024-10-06T10:57:32Z | |
| dc.date.issued | 2006 | |
| dc.description | Khrushchev, Sergey/0000-0002-8854-5317 | en_US |
| dc.description.abstract | A differential method discovered by Euler is justified and applied to give simple proofs to formulas relating important continued fractions with Laplace transforms. They include Stieltjes formulas and some Ramanujan formulas. A representation for the remainder of Leibniz's series as a continued fraction is given. We also recover the original Euler's proof for the continued fraction of hyperbolic cotangent. | en_US |
| dc.identifier.issn | 1068-9613 | |
| dc.identifier.scopus | 2-s2.0-33846993356 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14411/8739 | |
| dc.identifier.uri | https://doi.org/ | |
| dc.language.iso | en | en_US |
| dc.publisher | Kent State University | en_US |
| dc.relation.ispartof | Conference on Constructive Functions Tech-04 in honor of Edward B Saff -- NOV 07-09, 2004 -- Georgia Inst Technol, Atlanta, GA | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | continued fractions | en_US |
| dc.subject | Ramanujan formulas | en_US |
| dc.subject | Laplace transform | en_US |
| dc.title | On Euler's differential methods for continued fractions | en_US |
| dc.type | Conference Object | en_US |
| dspace.entity.type | Publication | |
| gdc.author.id | Khrushchev, Sergey/0000-0002-8854-5317 | |
| gdc.author.institutional | Khrushchev, Sergey | |
| gdc.author.scopusid | 7004133014 | |
| gdc.author.wosid | Khrushchev, Sergey/AAH-8676-2019 | |
| gdc.coar.access | metadata only access | |
| gdc.coar.type | text::conference output | |
| gdc.description.department | Atılım University | en_US |
| gdc.description.departmenttemp | Atilim Univ, Dept Math, TR-06836 Ankara, Turkey | en_US |
| gdc.description.endpage | 200 | en_US |
| gdc.description.publicationcategory | Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q3 | |
| gdc.description.startpage | 178 | en_US |
| gdc.description.volume | 25 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded - Conference Proceedings Citation Index - Science | |
| gdc.description.wosquality | Q2 | |
| gdc.identifier.wos | WOS:000247030900015 | |
| gdc.index.type | WoS | |
| gdc.index.type | Scopus | |
| gdc.scopus.citedcount | 1 | |
| gdc.virtual.author | Khrushchev, Sergey | |
| gdc.wos.citedcount | 2 | |
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