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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

On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials

Mathematics, 2020
The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are ...
Mohammed Abdalla, Mohra Zayed, Nasser Saad   +2 more
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

Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative

Mathematical and Computational Applications
In this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation.
Francisco Martinez, Mohammed K A Kaabar
exaly   +3 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   +4 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

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

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 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