scientific article; zbMATH DE number 7164311

zbMath1439.05011MaRDI QIDQ5214016

Burcin Simsek, Irem Kucukoglu, Yilmaz Simsek

Publication date: 6 February 2020

Full work available at URL: https://dergipark.org.tr/en/pub/tbtkmath/issue/50820/662524

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zbMATH Keywords

generating functionsStirling numbersprobability distributionbinomial coefficientsCatalan numberscombinatorial sumsApostol-Bernoulli numbersApostol-Euler numbersChu-Vandermonde convolution formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Combinatorial probability (60C05) Recurrences (11B37) Special sequences and polynomials (11B83) Real polynomials: analytic properties, etc. (26C05)

Related Items (17)

Implementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials ⋮ New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ Computational identities for extensions of some families of special numbers and polynomials ⋮ New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms ⋮ Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials ⋮ Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ The r‐hypergeometric distribution: Characterization, mathematical methods, simulations, and applications in sciences and engineering ⋮ A new class of generalized Fubini polynomials and their computational algorithms ⋮ Construction and computation of unified Stirling-type numbers emerging from \(p\)-adic integrals and symmetric polynomials ⋮ Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior ⋮ A new family of degenerate poly-Genocchi polynomials with its certain properties ⋮ Properties and graphical representations of the 2-variable form of the Simsek polynomials ⋮ A note on degenerate Genocchi and poly-Genocchi numbers and polynomials ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions ⋮ Unnamed Item ⋮ Some new identities and formulas for higher-order combinatorial-type numbers and polynomials ⋮ Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses

Cites Work

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• Modification and unification of the Apostol-type numbers and polynomials and their applications
• Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• Applications of an explicit formula for the generalized Euler numbers
• Catalan numbers, their generalization, and their uses
• Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series
• Partial derivative formulas and identities involving 2-variable Simsek polynomials
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Differential equations associated with degenerate Changhee numbers of the second kind
• On generating functions for Boole type polynomials and numbers of higher order and their applications
• Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
• Some series identities involving the generalized Apostol type and related polynomials
• Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions
• Inverse series relations and other expansions involving Humbert polynomials
• On the Lerch zeta function
• Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials
• Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers
• The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• Combinatorial identities associated with Bernstein type basis functions
• Univariate Discrete Distributions

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