# jacobi.p.quadrature: Perform Gauss Jacobi quadrature In gaussquad: Collection of functions for Gaussian quadrature

## 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 Jacobi P polynomials.

## Usage

 1 2 jacobi.p.quadrature(functn, rule, alpha = 0, beta = 0, lower = -1, upper = 1, 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 ultraspherical quadrature rule alpha numeric value for the first Jacobi polynomial parameter beta numeric value for the second Jacobi polynomial parameter lower numeric value for the lower limit of the integral with a default value of -1 upper numeric value for the upper limit of the integral with a default value of 1 weighted a boolean value which if true causes the ultraspherical weight function to be included in the integrand ... other arguments passed to the give function

## Details

The rule argument corresponds to an order n Jacobi polynomial, weight function and interval ≤ft[ { - 1,1} \right]. The lower and upper limits of the integral must be finite.

## Value

The value of definite integral evaluated using Gauss Jacobi quadrature

## Author(s)

Frederick Novomestky [email protected]

## 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.