If all you wanted was one derivative, i'd consider just an arccos and sines formula i gathered it was multiple derivatives desired
On Mon, Apr 6, 2015 at 8:04 AM, Paulo Jabardo <[email protected]> wrote: > 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 >> >
