New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms

DOI10.3906/mat-2008-24zbMath1493.05020OpenAlexW3104187149WikidataQ114022799 ScholiaQ114022799MaRDI QIDQ5099831

Burcin Simsek, Yilmaz Simsek, Irem Kucukoglu

Publication date: 26 August 2022

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-2008-24

zbMATH Keywords

generating functionStirling numberspartial differential equationscomputational algorithmsBernoulli polynomialsCatalan numbers\(p\)-adic integral

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Recurrences (11B37) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) General topics in the theory of algorithms (68W01) General theory for ordinary differential equations (34A99) General topics in partial differential equations (35A99)

Related Items (5)

Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations ⋮ Computational identities for extensions of some families of special numbers and polynomials ⋮ A new class of generalized Fubini polynomials and their computational algorithms ⋮ Unnamed Item ⋮ New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials

Cites Work

• \(q\)-Volkenborn integration
• Catalan numbers, their generalization, and their uses
• Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials
• 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
• An invariant \(p\)-adic \(q\)-integral on \(\mathbb Z _p\)
• The Cauchy numbers
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• Bernoulli polynomials of the second kind and their identities arising from umbral calculus
• Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers
• Singularity Analysis of Generating Functions
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• A note on Catalan numbers associated with p-adic integral on Zp
• Complex Analysis
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