# hermite.he.quadrature: Perform Gauss Hermite 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 hermite He polynomials.

## Usage

 1 2 hermite.he.quadrature(functn, rule, lower = -Inf, upper = Inf, 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 Hermite quadrature rule lower the lower limit of the integral with a default value of - ∞ upper the upper limit of the integral with a default value of + ∞ weighted a boolean value which if true causes the Hermite weight function to be included in the integrand ... other arguments passed to the give function

## Details

The rule argument corresponds to an order n Hermite polynomial, weight function and interval ≤ft( { - ∞ ,∞ } \right) The lower and upper limits of the integral must be infinite.

## Value

The value of definite integral evaluated using Gauss Hermite 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.