Results 11 to 20 of about 5,765 (234)

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\
Schmidt, Asmus L.
exaly   +4 more sources

A novel theory of Legendre polynomials

Mathematical and Computer Modelling, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MARTINELLI, Maria Renata, G. Dattoli, GERMANO, Bruna, RICCI, Paolo Emilio   +3 more
exaly   +4 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   +4 more sources

On polar Legendre polynomials [PDF]

Rocky Mountain Journal of Mathematics, 2010
We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect ...
Cabrera, H. Pijeira, Cruz, J. Bello, Romero, W. Urbina   +2 more
openaire   +5 more sources

Integral of Legendre polynomials and its properties [PDF]

Mathematics and Computational Sciences
This paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
doaj   +2 more sources

Generalized Legendre Polynomials

Journal of Mathematical Analysis and Applications, 1993
Let \((\lambda_ n)_{n\in\mathbb{N}}\) be a sequence of distinct real numbers with \(\lambda_ n>-1/2\). The authors orthogonalize the functions \(\{x^{\lambda_ 1},x^{\lambda_ 2},\dots\}\) with respect to the inner product \(\langle f,g\rangle:=\int_ 0^ 1 f(x)g(x)dx\) by using Gram-Schmidt-orthogonalization.
Mccarthy, P.C., Sayre, J.E., Shawyer, B.L.R.   +2 more
openaire   +3 more sources

On the interval Legendre polynomials

Journal of Computational and Applied Mathematics, 2003
This paper deals with the extension of the classical Legendre polynomials to the interval theory by considering the family of interval polynomials \(\mathbb L_{n,k}(x) \) satisfying, for each natural number \(k\), the recursive formula \(\mathbb L_{0,k}(x)=[1-\frac 1k,1+\frac 1k]\), \(\mathbb L_{1,k}(x)=[1-\frac 1k,1+\frac 1k]x\), \(\mathbb L_{n+1,k}(x)
Patrı́cio, F., Ferreira, J.A., Oliveira, F.   +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   +2 more sources

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   +6 more sources

Families of Legendre–Sheffer polynomials

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