Some identities on Bernoulli and Euler polynomials arising from orthogonality of Legendre polynomials

DOI10.1186/1029-242X-2012-227zbMath1279.33018OpenAlexW1993040312WikidataQ59272983 ScholiaQ59272983MaRDI QIDQ385852

Dae San Kim, Taekyun Kim, Seong-Hoon Rim

Publication date: 11 December 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2012-227

zbMATH Keywords

Legendre polynomialsBernoulli polynomialsEuler polynomials

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 (8)

Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials ⋮ Expressing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials by several orthogonal polynomials ⋮ Generalized Mixed Type Bernoulli-Gegenbauer Polynomials ⋮ Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds ⋮ DOUBLE EXPONENTIAL EULER–SINC COLLOCATION METHOD FOR A TIME–FRACTIONAL CONVECTION–DIFFUSION EQUATION ⋮ 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 ⋮ Bernoulli polynomials and their some new congruence properties

Cites Work

• A note on \(q\)-Bernstein polynomials
• Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials
• Finite summation formulas and congruences for Legendre and Jacobi polynomials
• Symmetry of power sum polynomials and multivariate fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\)
• Some integrals containing products of Legendre polynomials
• Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
• Complete sum of products of (h,q)-extension of Euler polynomials and numbers

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