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Continued fractions and inequalities about \(\left( 1+\frac{1}{x}\right)^x\)

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Publication:681276
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DOI10.1007/S00025-017-0752-YzbMath1429.41030OpenAlexW2754634020MaRDI QIDQ681276

Xiaoguang Wang, Dawei Lu, Jie Wei

Publication date: 30 January 2018

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-017-0752-y


zbMATH Keywords

inequalitiesrate of convergenceasymptotic expansioncontinued fraction


Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Continued fractions (11A55)





Cites Work

  • Unnamed Item
  • Continued fraction inequalities related to \((1+\frac{1}{x})^x\)
  • A new Stirling series as continued fraction
  • On new sequences converging towards the Euler-Mascheroni constant
  • On an infinite series for \((1 + 1/x)^{x}\) and its application
  • A continued fraction approximation of the gamma function
  • Sharp inequalities related to the constant \(e\)
  • A generated approximation related to Burnside's formula
  • Product Approximations via Asymptotic Integration
  • Very accurate estimates of the polygamma functions




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