Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials
type: Item
instance of: scholarly article
title: Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials
zbMATH Open document ID: 1258.33006
DOI: 10.1155/2012/957350
author: Taekyun Kim
author: Dae San Kim
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: Let \(\mathbf P_n = \{p(x) \in \mathbb R[x]\mid \deg p(x) \leq n\}\) be an inner product space with the inner product \(\langle p(x), q(x)\rangle = \int^\infty_0 x^\alpha e^{-x} p(x)q(x)\,dx\), where \(p(x), q(x) \in\mathbf P_n\) and \(\alpha \in \mathbb R\) with \(\alpha > -1\). In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for \(\mathbf P_n\). From those properties, we derive some interesting relations and identities of the extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 6116481
zbMATH Keywords: Extended Laguerre polynomials
zbMATH Keywords: Hermite numbers and polynomials
zbMATH Keywords: Bernoulli numbers and polynomials
zbMATH Keywords: Euler numbers and polynomials
Wikidata QID: Q58697171
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/957350
OpenAlex ID: W1983357429
cites work: Bilinear generating functions for Laguerre and Lauricella polynomials in several variables
cites work: Some generating functions for Laguerre polynomials
cites work: The product of several Hermite or Laguerre polynomials
cites work: A characterization of the Laguerre polynomials
cites work: On the Product of Two Laguerre Polynomials
cites work: A note on the Laguerre polynomials
cites work: Q4003595
cites work: Laguerre-based Appell polynomials: properties and applications
cites work: Hermite-based Appell polynomials: Properties and applications
cites work: Q3622741
cites work: Multivariate interpolation functions of higher-order \(q\)-Euler numbers and their applications
cites work: Q3001697
cites work: Q3171304
cites work: Q3172665
cites work: Q3003743
cites work: Q3514105
cites work: A new generating function of (\(q\)-) Bernstein-type polynomials and their interpolation function
cites work: New construction of weighted \((h, q)\)-Genocchi numbers and polynomials related to zeta type functions
cites work: A study on the fermionic \(p\)-adic \(q\)-integral representation on \(\mathbb Z_p\) associated with weighted \(q\)-Bernstein and \(q\)-Genocchi polynomials
cites work: Q3003992
cites work: Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials
cites work: Q3645776
cites work: Hermite polynomials and their applications associated with Bernoulli and Euler numbers
cites work: On q-Berstein and q-Hermite polynomials
cites work: Some formulae for the product of two Bernoulli and Euler polynomials
cites work: Congruence properties of Hermite and Laguerre polynomials
cites work: The p-adic generalized twisted (h,q)-euler-l-function and its applications
cites work: On finite sums of Laguerre polynomials
cites work: Some relations between twisted \((h, q)\)-Euler numbers with weight \(a\) and \(q\)-Bernstein polynomials with weight \(a\)
cites work: On the weighted q-Bernoulli numbers and polynomials
cites work: Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
cites work: Symmetry of power sum polynomials and multivariate fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\)
description: scientific article; zbMATH DE number 6116481