Some identities related to Eulerian polynomials and involving the Stirling numbers
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Publication:5155723
DOI10.2298/AADM171008014QzbMath1488.11061OpenAlexW4254026843WikidataQ129471812 ScholiaQ129471812MaRDI QIDQ5155723
Bai-Ni Guo, Feng Qi, Dongkyu Lim
Publication date: 8 October 2021
Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2298/aadm171008014q
generating functionStirling numberidentityopen problemEulerian polynomialhigher order Eulerian polynomial
Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68)
Related Items
Unnamed Item, Special values of the Bell polynomials of the second kind for some sequences and functions, Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function, Some properties of the Hermite polynomials, 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
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- An inequality involving the gamma and digamma functions
- An explicit formula for Bernoulli polynomials in terms of \(r\)-Stirling numbers of the second kind
- Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers
- Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function
- An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers
- A closed form for the Stirling polynomials in terms of the Stirling numbers
- Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations
- Simplifying differential equations concerning degenerate Bernoulli and Euler numbers
- Some identities of Eulerian polynomials arising from nonlinear differential equations
- 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
- Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
- Integral representations and properties of Stirling numbers of the first kind
- Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind
- Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
- Eulerian polynomials as moments, via exponential Riordan arrays
- Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
- Bounding the gamma function in terms of the trigonometric and exponential functions
- A completely monotonic function involving the gamma and tri-gamma functions
- A diagonal recurrence relation for the Stirling numbers of the first kind
- Simplifying coefficients in a family of nonlinear ordinary differential equations
- Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities
- 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
- Combinatorial Identities for Stirling Numbers