Hermite polynomials and their applications associated with Bernoulli and Euler numbers

DOI10.1155/2012/974632zbMath1248.11018OpenAlexW1969270341WikidataQ58700902 ScholiaQ58700902MaRDI QIDQ714309

Sang-Hun Lee, Dae San Kim, Taekyun Kim, Seong-Hoon Rim

Publication date: 19 October 2012

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/974632

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (12)

Identities associated with Milne-Thomson type polynomials and special numbers ⋮ Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials ⋮ Some recurrence formulas for the Hermite polynomials and their squares ⋮ An identity in commutative rings with unity with applications to various sums of powers ⋮ Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials ⋮ Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus ⋮ Expressing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials by several orthogonal polynomials ⋮ Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds ⋮ Computing integrals involved the Gaussian function with a small standard deviation ⋮ Formulas for Poisson-Charlier, Hermite, Milne-Thomson and other type polynomials by their generating functions and \(p\)-adic integral approach ⋮ Connection problem for sums of finite products of Chebyshev polynomials of the third and fourth kinds ⋮ Connection problem for sums of finite products of Legendre and Laguerre polynomials

Cites Work

• A note on the \(q\)-Euler numbers and polynomials with weak weight \(\alpha\)
• On the behavior of two variable twisted \(p\)-adic Euler \(q\)-\(l\)-functions
• A note on \(q\)-Bernstein polynomials
• Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials
• On linearization and connection coefficients for generalized Hermite polynomials
• \(p\)-adic distribution of the unification of the Bernoulli, Euler and Genocchi polynomials
• Construction a new generating function of Bernstein type polynomials
• Multiplication formulas for products of Bernoulli and Euler polynomials
• A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
• Hermite polynomials
• Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
• Old and new results about relativistic Hermite polynomials
• Orthogonality of Hermite polynomials in superspace and Mehler type formulae
• Note on the Integral of the Product of Several Bernoulli Polynomials

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