On Euler's differential methods for continued fractions

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Date

2006

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Kent State University

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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.

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Khrushchev, Sergey/0000-0002-8854-5317
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Khrushchev, Sergey ORCID logo

Keywords

continued fractions, Ramanujan formulas, Laplace transform

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Q3

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Q3

Source

Conference on Constructive Functions Tech-04 in honor of Edward B Saff -- NOV 07-09, 2004 -- Georgia Inst Technol, Atlanta, GA

Volume

25

Issue

Start Page

178

End Page

200

URI

https://hdl.handle.net/20.500.14411/8739

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