A diagonal recurrence relation for the Stirling numbers of the first kind

DOI10.2298/AADM170405004QzbMath1488.11060MaRDI QIDQ5155703

Feng Qi, Bai-Ni Guo

Publication date: 8 October 2021

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

complete monotonicityStirling numbers of the first kindLerch transcendentdiagonal recurrence relationinhomogeneous linear ordinary dierential equation

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Laplace transform (44A10) Hurwitz and Lerch zeta functions (11M35)

Related Items (22)

Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions ⋮ MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function ⋮ Unnamed Item ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ Computation of several Hessenberg determinants ⋮ Some identities related to Eulerian polynomials and involving the Stirling numbers ⋮ An explicit formula for derivative polynomials of the tangent function ⋮ Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions ⋮ Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function ⋮ Some properties of the Hermite polynomials ⋮ Some identities for a sequence of unnamed polynomials connected with the Bell polynomials ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi ⋮ Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind ⋮ Some symmetric identities involving the Stirling polynomials under the finite symmetric group ⋮ Unnamed Item ⋮ A closed-form expression of a remarkable sequence of polynomials originating from a family of entire functions connecting the Bessel and Lambert functions ⋮ Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences ⋮ Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials ⋮ Closed formulas and identities on the Bell polynomials and falling factorials. ⋮ Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials

Uses Software

• DLMF

Cites Work

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