Results 21 to 30 of about 516,382 (294)

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

Exceptional Legendre Polynomials and Confluent Darboux Transformations

, 2021
Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial ...
M. A. García‐Ferrero, Ruprecht-Karls-Universit, D. Gómez‐Ullate, R. Milson   +3 more
semanticscholar   +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

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   +1 more source

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   +2 more sources

On Some Relations between the Hermite Polynomials and Some Well-Known Classical Polynomials and the Hypergeometric Function.

مجلة العلوم البحتة والتطبيقية, 2020
The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
doaj   +1 more source

A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula [PDF]

, 2013
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree $N$ polynomial in $O(N(\log N)^{2}/ \log \log N)$ operations is derived.
Hale, Nicholas, Townsend, Alex
core   +1 more source

Certain integrals involving generalized Mittag-Leffler type functions

Vojnotehnički Glasnik, 2022
Introduction/purpose: Certain integrals involving the generalized MittagLeffler function with different types of polynomials are established. Methods: The properties of the generalized Mittag-Leffler function are used in conjunction with different ...
Sirazul Haq, Maggie Aphane, Mohammad Saeed Khan, Nicola Fabiano   +3 more
doaj   +1 more source

Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations

Communications, 2010
In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre
Vladimir Guldan, Mariana Marcokova
doaj   +1 more source

Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation

Journal of Applied Sciences and Environmental Management, 2006
In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient.
FO Akinpelu, LA Adetunde, EO Omidiora
doaj   +1 more source