Some identities on Bernoulli and Hermite polynomials associated with Jacobi polynomials

DOI10.1155/2012/584643zbMath1254.33011OpenAlexW2064560320WikidataQ58700656 ScholiaQ58700656MaRDI QIDQ714273

Dae San Kim, Dmitry V. Dolgy, Taekyun Kim

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/10.1155/2012/584643

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 (9)

Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials ⋮ Some identities involving Gegenbauer polynomials ⋮ Expressing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials by several orthogonal polynomials ⋮ Some identities involving generalized Gegenbauer polynomials ⋮ Fractional differential equations for the generalized Mittag-Leffler function ⋮ Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds ⋮ Unnamed Item ⋮ 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

• Special functions related to Dedekind-type DC-sums and their applications
• Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials
• Some identities on the \(q\)-Genocchi polynomials of higher-order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
• An identity of the symmetry for the Frobenius-Euler polynomials associated with the fermionic \(p\)-adic invariant \(q\)-integrals on \({\mathbf Z}_p\)
• \(q\)-Volkenborn integration
• Some identities on the twisted \((h,q)\)-Genocchi numbers and polynomials associated with \(q\)-Bernstein polynomials
• Finite summation formulas and congruences for Legendre and Jacobi polynomials
• Multivariate interpolation functions of higher-order \(q\)-Euler numbers and their applications
• A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
• Symmetry of power sum polynomials and multivariate fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\)
• On Euler-Barnes multiple zeta functions
• The generating function for the Jacobi polynomial
• Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
• On the weighted q-Bernoulli numbers and polynomials
• Twisted Dedekind Type Sums Associated with Barnes' Type Multiple Frobenius-Euler l-Functions
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