jacobi {rjacobi}R Documentation

Jacobi Polynomials

Description

Computes Jacobi polynomials

Usage

y = jacobi(x,n,a=0,b=0)

Arguments

x A vector 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 Jacobi Polynomials are computed from the recurrence formula:

a^1_n P_{n+1}^{α,β}(x) = (a^2_n + a^3_n x)P_n^{α,β}(x) - a^4_n P_{n-1}^{α,β}(x)

Value

A vector containing the values of the computed 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 <- jacobi(x, 5, 0, 0)
plot(x, y, ty='l')



[Package rjacobi version 0.9.2 Index]