Results 31 to 40 of about 6,156 (296)

Some further results on Legendre numbers

International Journal of Mathematics and Mathematical Sciences, 1988
The Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm−1, in the previous column down to Pnm and in terms of those, Pkm, above but in the same column. Other results are given for numbers close to a given number. The limit of the quotient
Paul W. Haggard
doaj   +1 more source

A new Fortran 90 program to compute regular and irregular associated Legendre functions [PDF]

, 2019
We present a modern Fortran 90 code to compute the regular Plm(x) and irregular Qlm(x) associated Legendre functions for all x∈(-1,+1) (on the cut) and |x|>1 and integer degree (l) and order (m).
Barry I. Schneider (8093585), Amparo Gil (330271), Klaus Bartschat (8093588), Xiaoxu Guan (561881), Javier Segura (6993842)   +4 more
core   +1 more source

An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition

Open Mathematics, 2023
In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce
Zou Shuimu, Zhang Jun
doaj   +1 more source

Evaluation of the Gaunt Coefficients by Using Recurrence Relations for Spherical Harmonics

Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2023
The Gaunt coefficient is one of the important coefficients to be known for calculating molecular integrals in quantum theory of coupling of three angular momenta.
Selda Özay
doaj   +1 more source

Definite Integrals using Orthogonality and Integral Transforms

Symmetry, Integrability and Geometry: Methods and Applications, 2012
We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Howard S. Cohl, Hans Volkmer
doaj   +1 more source

An Expansion in Terms of Associated Legendre Functions [PDF]

Proceedings of the Glasgow Mathematical Association, 1952
If the right-hand side of the expansionis integrated m times from 1 to µ, it ...
openaire   +1 more source

A code to calculate high order legendre polynomials and functions [PDF]

, 2013
En este trabajo se presenta, con una finalidad pedagógica, un método para evaluar funciones y polinomios de Legendre. El método utiliza relaciones de recurrencia estables que involucran a estas funciones.In this paper we present, with a pedagogical aim ...
Hernández, E., Fernández de Córdoba, P., Selezneva, I. A, Pérez Quiles, J.   +3 more
core   +1 more source

Covariance function of Legendre polynomials for the modeling of Polled Nellore cattle growth in northern Brazil

Semina: Ciências Agrárias, 2019
This study aimed to compare random regression models fitted by Legendre orthogonal polynomials and determine which best fits changes in Nellore cattle growth parameters.
Diego Helcias Cavalcante, Severino Cavalcante Sousa Júnior, Luciano Pinheiro da Silva, Carlos Henrique Mendes Malhado, Raimundo Martins Filho, José Elivalto Guimarães Campêlo, Karina Rodrigues Santos   +6 more
doaj   +1 more source

Recurrence relations for the indefinite integrals of the associated Legendre functions [PDF]

, 1982
Two recurrence relations are derived for the computation of the integral of the associated Legendre functions of real argument and integer order and degree.
A. R. DiDonato
core   +1 more source

On Multivariate Picard–Fuchs Systems and Equations

J, 2023
In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting properties of such
Alexander G. Aleksandrov
doaj   +1 more source