Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series

DOI10.1186/s13660-019-2006-xzbMath1499.05050OpenAlexW2938403394WikidataQ128273598 ScholiaQ128273598MaRDI QIDQ2067780

Yilmaz Simsek, Ji Suk So

Publication date: 19 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-019-2006-x

zbMATH Keywords

functional equationgenerating functionStirling numbersbinomial coefficientBonferroni inequalitiesEuler numbers and polynomialsPeters polynomialsBoole polynomialsspecial numbers and polynomialsChanghee numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Special sequences and polynomials (11B83) Inequalities for trigonometric functions and polynomials (26D05)

Related Items (9)

Two Explicit Formulas for Degenerate Peters Numbers and Polynomials ⋮ Unnamed Item ⋮ Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers ⋮ Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior ⋮ Derivation of computational formulas for Changhee polynomials and their functional and differential equations ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions ⋮ Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers ⋮ On generating functions for Boole type polynomials and numbers of higher order and their applications

Cites Work

• Barnes-type Peters polynomial with umbral calculus viewpoint
• Application of a composition of generating functions for obtaining explicit formulas of polynomials
• Sum of the reciprocals of the binomial coefficients
• Stirling numbers of the second kind and Bonferroni's inequalities
• Applications of an explicit formula for the generalized Euler numbers
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
• On the Lerch zeta function
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications
• On a family of special numbers and polynomials associated with Apostol-type numbers and polynomials and combinatorial numbers
• On Boole-type combinatorial numbers and polynomials
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