Share:

### Description

This function evaluates the integral of the given function between the lower and upper limits using the weight and abscissa values specified in the rule data frame. The quadrature formula uses the weight function for Chebyshev S polynomials.

### Usage

 1 2 chebyshev.s.quadrature(functn, rule, lower = -2, upper = 2, weighted = TRUE, ...)

### Arguments

 functn an R function which should take a numeric argument x and possibly some parameters. The function returns a numerical vector value for the given argument x. rule a data frame containing the order n Chebyshev quadrature rule lower numeric value for the lower limit of the integral with a default value of -2 upper numeric value for the upper limit of the integral with a default value of +2 weighted boolean value which if true causes the Chebyshev weight function to be included in the integrand ... other arguments passed to the give function

### Details

The rule argument corresponds to an order n Chebyshev polynomial, weight function and interval ≤ft[ { - 2,2} \right]. The lower and upper limits of the integral must be finite.

### Value

The value of definite integral evaluated using Gauss Chebyshev quadrature

### Author(s)

Frederick Novomestky fnovomes@poly.edu

### References

Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York.

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.

Stroud, A. H., and D. Secrest, 1966. Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, NJ.