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Families of Legendre–Sheffer polynomials

Mathematical and Computer Modelling, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Subuhi Khan
exaly   +3 more sources

Insight into Genome-Wide Associations of Growth Trajectories Using a Hierarchical Non-Linear Mixed Model [PDF]

Biology
In applying a hierarchical mixed model to genome-wide association analysis (GWAS) of longitudinal data, dimensionality reduction through modeling repeated measurements improves both computational efficiency and statistical power. Legendre polynomials can
Ying Zhang, Li’ang Yang, Weiguo Cui, Runqing Yang   +3 more
doaj   +2 more sources

A novel theory of Legendre polynomials

Mathematical and Computer Modelling, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P E Ricci
exaly   +3 more sources

Generalized q-Legendre polynomials

Journal of Computational and Applied Mathematics, 1993
The author finds the polynomials \(u_ n\) satisfying the 3-term recursion: \[ (1-q^{n+1}) (1+q^ n) u_{n+1} - f_ nu_ n + q^{2n- 1} (1-q^ n) (1+q^{N+1}) u_{n-1} = 0, \] where \[ f_ n = (1- q^{2n+1}) \left( 2q^ n-(1+q^ n) (1+q^{n+1}) \sum_{j=0}^ nq^{-jn} \left[ {n \over j} \right]_ q \left[ {n+j \over j} \right]_ qx_ j \right). \] For \(x_ 0=x\), \(x_ j=0\
exaly   +3 more sources

Properties of Clifford-Legendre Polynomials [PDF]

Advances in Applied Clifford Algebras, 2022
Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra ${\mathbb R}_m$.
Ghaffari, Hamed Baghal, Hogan, Jeffrey A., Lakey, Joseph D.   +2 more
openaire   +3 more sources

Discrete Hypergeometric Legendre Polynomials

Mathematics, 2021
A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials.
Tom Cuchta, Rebecca Luketic
doaj   +1 more source

On the Elementary Symmetric Polynomials and the Zeros of Legendre Polynomials

Journal of Mathematics, 2022
In this paper, we seek to present some new identities for the elementary symmetric polynomials and use these identities to construct new explicit formulas for the Legendre polynomials.
Maryam Salem Alatawi
doaj   +1 more source

On the estimation of functions belonging to Lipschitz class by block pulse functions and hybrid Legendre polynomials

Karpatsʹkì Matematičnì Publìkacìï, 2020
In this paper, block pulse functions and hybrid Legendre polynomials are introduced. The estimators of a function $f$ having first and second derivative belonging to $Lip_\alpha[a,b]$ class, $0 < \alpha \leq 1$, and $a$, $b$ are finite real numbers, by ...
S. Lal, V.K. Sharma
doaj   +1 more source

About the Legendre type operators [PDF]

E3S Web of Conferences, 2021
The article considers Legendre type operators acting in the corresponding weight separable Hilbert spaces. The choice of these spaces is due to the fact that these operators preserve all properties of the Legendre operator acting on L2 (-1,1).
Maleko Evgeny
doaj   +1 more source

An Orthogonality Property of the Legendre Polynomials [PDF]

Constructive Approximation, 2016
We give a remarkable additional orthogonality property of the classical Legendre polynomials on the real interval $[-1,1]$: polynomials up to degree $n$ from this family are mutually orthogonal under the arcsine measure weighted by the degree-$n$ normalized Christoffel function.
BOS, LEONARD PETER, Levenberg, N, Narayan, A, Piazzon, F.   +3 more
openaire   +5 more sources