djacobi {rjacobi} | R Documentation |
Calculates the derivative of the nth order Jacobi polynomials at an array of np points given by the vector x.
y = djacobi(x, n, a=0.0, b=0.0)
x |
A vector of length np containing the points where the polynomials should be calculated. -1<= x_i <= 1 |
n |
Order of Jacobi polynomial to be calculated |
a |
α parameter of Jacobi polynomial. Defaults to 0 |
b |
β parameter of Jacobi polynomial. Defaults to 0 |
The derivative of the Jacobi Polynomials is computed from the following equation:
frac{d}{dx}P^{α,β}_n(x) = frac{1}{2}(α + β + n + 1) P_n^{α+1,β+1}(x)
A vector containing the values of the computed derivatives of Jacobi Polynomials
Abramowitz, Milton and Stegun, Irene (editors); "Handbook of Mathematical functions", Dover Publications 1965.
Karniadakis, George Em and Sherwin, Spencer; "Spectral/hp Element Methods for Computational Fluid Dynamics", Oxford Science Publications, 2nd edition, 2005.
## Example to plot the 5th order Jacobi Polynomial x <- seq(-1, 1, len=101) y <- djacobi(x, 5, 0, 0) plot(x, y, ty='l')