Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses

DOI10.2298/AADM201017009KzbMath1499.05041MaRDI QIDQ5028837

Yilmaz Simsek, Irem Kucukoglu

Publication date: 10 February 2022

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

zbMATH Keywords

generating functionsintegral transformprobability distribution functionsspecial numbers and polynomialscombinatorial numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Special sequences and polynomials (11B83) Basic linear algebra (15A99)

Related Items (1)

Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions

Cites Work

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• Cyclic derangements
• Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers
• A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
• Operational formulas connected with two generalizations of Hermite polynomials
• Multidimensional extensions of the Bernoulli and Appell polynomials
• Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials
• Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions
• Some theorems on Bernoulli numbers of higher order
• On zero product determined algebras
• Integrals Don’t Have Anything to Do with Discrete Math, Do They?
• Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• A new family of combinatorial numbers and polynomials associated with peters numbers and polynomials
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
• A new class of polynomials associated with Bernstein and beta polynomials

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