There is a recurrence relation for the derivatives but it involves the Chebyshev polynomials of second kind.
Chebyshev polynomials of first kind: T_0(x) = 1 T_1(x) = x T_(n+1)(x) = 2x.T_n(x) - T_(n-1)(x) Chebyshev polynomials of second kind: U_0(x) = 1 U_1(x) = 2x U_(n+1)(x) = 2x.U_n(x) - U_(n-1)(x) Derivative: dT_n/dx = n.U_(n-1)(x) Source http://en.wikipedia.org/wiki/Chebyshev_polynomials NIST Handbook of mathematical functions: http://dlmf.nist.gov/18.9 Paulo PS I have a package https://github.com/pjabardo/Jacobi.jl I will try to insert Chebyshev polynomials (and derivatives - very usefull for spectral methods) today. On Thursday, April 2, 2015 at 11:38:48 AM UTC-3, Tamas Papp wrote: > > Hi, > > Can someone point me to some Julia code that calculates a matrix for the > derivatives of the Chebyshev polynomials T_j, at given values, ie > > d^k T_i(x_j) / dx^k for i=1,..n, j for some and vector x. > > The Chebyshev polynomials themselves are very easy to calculate using > the recurrence relation, but derivatives are not. Alternatively, maybe > this can be extracted from ApproxFun but I have not found a way. > > Best, > > Tamas >
