Philips, "On the Legendre Coefficients of a General-Order Derivative of an Infinitely Differential Function", IMA Journal of Numerical Analysis, 1988, Volume 8, p. is the associated Legendre function with the following definition, where P n is the standard Legendre polynomial of degree n.
![legendre polynomials matlab 2014a legendre polynomials matlab 2014a](https://i.ytimg.com/vi/1iXvMffmfhA/maxresdefault.jpg)
This is much more stable than converting to the monomial base and applying Horner's rule. Finally, in order to use them as polynomials for Gaussian quadrature, you will need the derivative polynomials too. All I need is is the simple Legendre polynomial of degrees 0-299, which corresponds to the first element in the array that this function returns. If $f(x)$ is an infinitely differentiable function defined on the interval $$ and its Legendre expansion is given by $f(x) = \sum_(x)$ is best done using the Clenshaw-Smith algorithm (see Smith's paper). I see in MATLAB that you can call legendre(n,X) and it returns the associated legendre polynomials. The polynomial degree in a mesh interval is increased if the Legendre polynomial coefficient decay rate exceeds a user-specified threshold. The format of the output is such that: Each row. Calculate the second-degree Legendre function values of a vector. Type 2 represents an analytic continuation of type 1 outside the unit circle. Type 1 is defined only for within the unit circle in the complex plane. The symbolic form of type 1 involves, of type 2 involves, and of type 3 involves. Philips in 1988 proved the following relationship: Use the legendre function to operate on a vector and then examine the format of the output. LegendreP n, m, a, z gives Legendre functions of type a.