Computational identities for extensions of some families of special numbers and polynomials

DOI10.3906/mat-2101-83zbMath1493.11059OpenAlexW3200420427MaRDI QIDQ5099164

Irem Kucukoglu, Yilmaz Simsek

Publication date: 31 August 2022

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

Full work available at URL: https://doi.org/10.3906/mat-2101-83

zbMATH Keywords

generating functionsCatalan numbersStirling approximationcombinatorial numbersspecial numbers and polynomials\(p\)-adic integrals

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Other functions defined by series and integrals (33E20) Special sequences and polynomials (11B83) Real polynomials: analytic properties, etc. (26C05)

Related Items (1)

Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations

Cites Work

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• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• \(q\)-Volkenborn integration
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• Catalan numbers, their generalization, and their uses
• Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and \(p\)-adic integrals
• Differential equations associated with Catalan-Daehee numbers and their applications
• A new approach to Catalan numbers using differential equations
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers
• 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
• On the Lerch zeta function
• An Introduction to Catalan Numbers
• 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
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• NOTE ON APOSTOL-DAEHEE POLYNOMIALS AND NUMBERS
• New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms
• Peters type polynomials and numbers and their generating functions: Approach with p‐adic integral method
• A note on Catalan numbers associated with p-adic integral on Zp
• Complex Analysis

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