Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind

DOI10.3934/math.2019.2.170zbMath1429.34025OpenAlexW2743080976WikidataQ128389968 ScholiaQ128389968MaRDI QIDQ2335325

Feng Qi, Da-Wei Niu, Bai-Ni Guo

Publication date: 14 November 2019

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

Full work available at URL: https://doi.org/10.3934/math.2019.2.170

zbMATH Keywords

inversion formulaordinary differential equationsimplificationStirling number of the second kindStirling number of the first kindcoefficientBell polynomial of the second kindFa`a di Bruno formulahigher order Bernoulli number of the second kind

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Linear ordinary differential equations and systems (34A30) Special sequences and polynomials (11B83) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (6)

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 a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• 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
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
• A diagonal recurrence relation for the Stirling numbers of the first kind
• Some identities related to Eulerian polynomials and involving the Stirling numbers
• Simplifying and finding ordinary differential equations in terms of the stirling numbers
• Simplifying coefficients in a family of nonlinear ordinary differential equations
• AN INTEGRAL REPRESENTATION, SOME INEQUALITIES, AND COMPLETE MONOTONICITY OF THE BERNOULLI NUMBERS OF THE SECOND KIND
• A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind
• Combinatorial Identities for Stirling Numbers

This page was built for publication: Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind