How do you use Legendre in Matlab?
Use the legendre function to operate on a vector and then examine the format of the output. Calculate the second-degree Legendre function values of a vector. The format of the output is such that: Each row contains the function value for different values of m (the order of the associated Legendre function)
What is associated Legendre differential equation?
The Legendre ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace’s equation (and related partial differential equations) in spherical coordinates.
Why do we use Legendre equations?
For example, Legendre and Associate Legendre polynomials are widely used in the determination of wave functions of electrons in the orbits of an atom [3], [4] and in the determination of potential functions in the spherically symmetric geometry [5], etc.
What is exponent Matlab?
Description. The exp function is an elementary function that operates element-wise on arrays. Its domain includes complex numbers. Y = exp(X) returns the exponential for each element of X . For complex , it returns the complex exponential.
What are the singular points of Legendre differential equation?
Legendre Equation: The points x = ±1 are singular points, since P(x) = 1- x2 is zero there. All other points are ordinary points.
What is Rodrigues formula for Legendre polynomial?
In mathematics, Rodrigues’ formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by Olinde Rodrigues (1816), Sir James Ivory (1824) and Carl Gustav Jacobi (1827). The term is also used to describe similar formulas for other orthogonal polynomials.
How to find Legendre polynomials of degrees 1 and 2?
Find Legendre Polynomial with Vector and Matrix Inputs. Find the Legendre polynomials of degrees 1 and 2 by setting n = [1 2]. syms x legendreP([1 2],x) ans = [ x, (3*x^2)/2 – 1/2] legendreP acts element-wise on n to return a vector with two elements.
How are Legendre polynomials related to the weight function?
Legendre Polynomial. The Legendre polynomials are defined as. The Legendre polynomials satisfy the recursion formula. The Legendre polynomials are orthogonal on the interval [-1,1] with respect to the weight function w(x) = 1, where. The relation with Gegenbauer polynomials G (n,a,x) is.
How are Legendre polynomials related to Jacobi polynomials?
The Legendre polynomials are defined as. The Legendre polynomials satisfy the recursion formula. The Legendre polynomials are orthogonal on the interval [-1,1] with respect to the weight function w(x) = 1, where. The relation with Gegenbauer polynomials G(n,a,x) is. The relation with Jacobi polynomials P(n,a,b,x) is.