A-Z-Leitfaden über Thermodynamik, Wärme- und Stoffübertragung und Strömungstechnik
Deutsch English Русский 中文 Português Español Français Über unser Angebot Redaktion Kontakt Zugriff Begell House
View in A-Z Index

Legendre type polynomials or spherical polynomials are polynomials orthogonal on the interval [−1, 1] with unit weight.

Legendre polynomials are defined by:

(1)

The representation

(2)

is valid for Legendre polynomials.

Legendre polynomials are bounded on the interval [−1, 1] by the solution of the differential Legendre equation

(3)

which appears in problems of heat conduction when solving the Laplace equation in spherical coordinates by the separation of variables method.

The following recurrent relations are valid for Legendre polynomials

(4)

Legendre polynomials have n different real roots. They all lie on the interval [−1, 1]. For Legendre polynomials the representation

(5)

are valid.

Also expressed in terms of Legendre polynomials are adjoint functions, which are often used in soving problems of radiation heat transfer

(6)
Anzahl der Aufrufe: 13980 Artikel hinzugefügt: 2 February 2011 Letzte Bearbeitung des Artikels: 11 February 2011 © Copyright 2010-3921 Zurück nach oben
A-Z-Index Autoren / Redakteure Semantische Karte Visuelle Galerie Einen Beitrag leisten Guest