Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers

DOI10.1007/S13398-020-00899-ZzbMath1484.11072OpenAlexW3041167539MaRDI QIDQ783263

Yilmaz Simsek, Damla Gun

Publication date: 12 August 2020

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-020-00899-z

zbMATH Keywords

series representationsgenerating functionintegral representationsStirling numbers of second kindLaplace transformationEulerian numbersCatalan numbersBernoulli polynomials of higher orderBernoulli numbers of higher order

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Real polynomials: analytic properties, etc. (26C05)

Related Items (11)

Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations ⋮ Parametric binomial sums involving harmonic numbers ⋮ New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ A special approach to derive new formulas for some special numbers and polynomials ⋮ Modification exponential Euler type splines derived from Apostol-Euler numbers and polynomials of complex order ⋮ Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions ⋮ Closed formulas and determinantal expressions for higher-order Bernoulli and Euler polynomials in terms of Stirling numbers ⋮ New computational formulas for special numbers and polynomials derived from applying trigonometric functions to generating functions ⋮ Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses

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• Integral presentations of Catalan numbers
• Permutations and sequences with repetitions by number of increases

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