\(q\)-Bernstein polynomials associated with \(q\)-Stirling numbers and Carlitz's \(q\)-Bernoulli numbers

DOI10.1155/2010/150975zbMath1208.11029arXiv1009.3439OpenAlexW1760824630WikidataQ58649758 ScholiaQ58649758MaRDI QIDQ624465

Juan-Miguel Gracia

Publication date: 9 February 2011

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3439

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items

A survey of results on the limit \(q\)-Bernstein operator ⋮ A note on some properties of the weighted \(q\)-Genocchi numbers and polynomials ⋮ On the \(q\)-Bernoulli numbers and polynomials with weight \(\alpha\) ⋮ Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials ⋮ Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\) ⋮ A study on the fermionic \(p\)-adic \(q\)-integral representation on \(\mathbb Z_p\) associated with weighted \(q\)-Bernstein and \(q\)-Genocchi polynomials ⋮ A new class of polynomials associated with Bernstein and beta polynomials ⋮ Some identities on Bernstein polynomials associated with \(q\)-Euler polynomials

Cites Work

• A note on \(q\)-Bernstein polynomials
• \(q\)-Volkenborn integration
• A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
• Note on the Euler \(q\)-zeta functions
• \(q\)-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients
• A note on the modified \(q\)-Bernstein polynomials
• Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
• Barnes-type multipleq-zeta functions andq-Euler polynomials
• A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
• Unnamed Item

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