A new approach to \(q\)-Bernoulli numbers and \(q\)-Bernoulli polynomials related to \(q\)-Bernstein polynomials

DOI10.1155/2010/951764zbMath1229.11034OpenAlexW1978305550WikidataQ59267520 ScholiaQ59267520MaRDI QIDQ537160

Dilek Erdal, Serkan Araci, Mehmet Acikgoz

Publication date: 19 May 2011

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/951764

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Zeta functions and (L)-functions (11S40)

Related Items

Some identities of Bernoulli, Euler and Abel polynomials arising from umbral calculus ⋮ A note on \((p,q)\)-Bernstein polynomials and their applications based on \((p,q)\)-calculus ⋮ Differential equations associated with generalized Bell polynomials and their zeros ⋮ A new construction on the \(q\)-Bernoulli polynomials ⋮ \(q\)-Bernoulli numbers and \(q\)-Bernoulli polynomials revisited ⋮ Approximation of Durrmeyer type operators depending on certain parameters ⋮ \(\lambda\)-\(q\)-Sheffer sequence and its applications ⋮ Higher-order Bernoulli, Euler and Hermite polynomials ⋮ A note on the modified \(q\)-Bernstein polynomials for functions of several variables and their reflections on \(q\)-Volkenborn integration ⋮ A note on degenerate poly-Bernoulli numbers and polynomials ⋮ \(q\)-Bernoulli polynomials and \(q\)-umbral calculus ⋮ A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials ⋮ Some identities of Carlitz degenerate Bernoulli numbers and polynomials ⋮ On \(p\)-adic fermionic integrals of \(q\)-Bernstein polynomials associated with \(q\)-Euler numbers and polynomials

Cites Work

• On \(p\)-adic analogue of \(q\)-Bernstein polynomials and related integrals
• \(q\)-Volkenborn integration
• Non-Archimedean \(q\)-integrals associated with multiple Changhee \(q\)-Bernoulli polynomials
• Analytic continuation of multiple \(q\)-zeta functions and their values at negative integers
• Power series and asymptotic series associated with the \(q\)-analog of the two-variable \(p\)-adic \(L\)-function
• On the \(q\)-extension of Euler and Genocchi numbers
• A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
• Note on the Euler \(q\)-zeta functions
• On multiple interpolation functions of the Nörlund-type \(q\)-Euler polynomials
• \(q\)-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients
• On \(p\)-adic \(q\)-\(L\)-functions and sums of powers
• A note on the modified \(q\)-Bernstein polynomials
• \(q\)-Bernoulli numbers and polynomials
• Some identities on the q-Bernstein polynomials, q-Stirling number and q-Bernoulli numbers
• Degenerate Bernstein polynomials
• Quantum calculus
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A new approach to \(q\)-Bernoulli numbers and \(q\)-Bernoulli polynomials related to \(q\)-Bernstein polynomials