Simplifying differential equations concerning degenerate Bernoulli and Euler numbers

DOI10.1016/j.trmi.2017.08.001zbMath1391.34028OpenAlexW2745979020MaRDI QIDQ1749328

Jing-Lin Wang, Bai-Ni Guo, Feng Qi

Publication date: 16 May 2018

Published in: Transactions of A. Razmadze Mathematical Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.trmi.2017.08.001

zbMATH Keywords

Euler numbernonlinear ordinary differential equationBernoulli numberStirling number of the second kindStirling number of the first kind

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Nonlinear ordinary differential equations and systems (34A34)

Related Items (9)

Unnamed Item ⋮ Causal difference equations with upper and lower solutions in the reverse order ⋮ Some identities related to Eulerian polynomials and involving the Stirling numbers ⋮ Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind ⋮ Unnamed Item ⋮ Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials

Cites Work

• Higher recurrences for Apostol-Bernoulli-Euler numbers
• Closed formulas for computing higher-order derivatives of functions involving exponential functions
• Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials
• A closed form for the Stirling polynomials in terms of the Stirling numbers
• Complete monotonicity of functions connected with the exponential function and derivatives
• Explicit formulas and recurrence relations for higher order Eulerian polynomials
• Some identities and an explicit formula for Bernoulli and Stirling numbers
• Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
• Integral representations and properties of Stirling numbers of the first kind
• Some identities involving exponential functions and Stirling numbers and applications
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION
• Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
• Some identities of degenerate Daehee numbers arising from certain differential equations
• A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind
• Diagonal recurrence relations for the Stirling numbers of the first kind

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