Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind

DOI10.7153/mia-19-23zbMath1333.11027arXiv1402.2040OpenAlexW1775480756MaRDI QIDQ2794823

Feng Qi

Publication date: 11 March 2016

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2040

zbMATH Keywords

monotonicityinequalityFaà di Bruno formulaStirling number of the second kindBell polynomials of the second kinddiagonal recurrence relationlogarithmically convex sequence

Mathematics Subject Classification ID

Partitions of sets (05A18) Bell and Stirling numbers (11B73) Recurrences (11B37)

Related Items (15)

Some properties of the Schröder numbers ⋮ Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers ⋮ A closed form for the Stirling polynomials in terms of the Stirling numbers ⋮ Increasing property and logarithmic convexity of functions involving Dirichlet lambda function ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations ⋮ Closed formulas for computing higher-order derivatives of functions involving exponential functions ⋮ A diagonal recurrence relation for the Stirling numbers of the first kind ⋮ Some identities related to Eulerian polynomials and involving the Stirling numbers ⋮ Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers ⋮ Explicit formulas and recurrence relations for higher order Eulerian polynomials ⋮ Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios ⋮ 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 ⋮ Some symmetric identities involving the Stirling polynomials under the finite symmetric group

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