djacobi {rjacobi}R Documentation

Derivative of Jacobi Polynomials

Description

Calculates the derivative of the nth order Jacobi polynomials at an array of np points given by the vector x.

Usage

y = djacobi(x, n, a=0.0, b=0.0)

Arguments

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

Details

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)

Value

A vector containing the values of the computed derivatives of Jacobi Polynomials

References

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.

Examples


## 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')


[Package rjacobi version 0.9.2 Index]