Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials

DOI10.1007/s00009-017-0939-1zbMath1427.11023OpenAlexW2619444248MaRDI QIDQ1674224

Bai-Ni Guo, Feng Qi

Publication date: 1 November 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-017-0939-1

zbMATH Keywords

Euler numberspecial valueexplicit formuladouble sumEuler polynomialBell polynomial of the second kindpropertyweighted Stirling number

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Special polynomials in general fields (12E10) Exponential and trigonometric functions (33B10)

Related Items (27)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Several closed expressions for the Euler numbers
• Explicit expressions for a family of the Bell polynomials and applications
• An explicit formula for Bernoulli polynomials in terms of \(r\)-Stirling numbers of the second kind
• Derivatives of tangent function and tangent numbers
• The \(r\)-Stirling numbers
• Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
• Certain identities, connection and explicit formulas for the Bernoulli and Euler numbers and the Riemann zeta-values
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• Eulerian Numbers and Polynomials
• A Special Class of Bell Polynomials
• SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS
• Double Series for the Bernoulli and Euler Numbers
• Diagonal recurrence relations for the Stirling numbers of the first kind

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