# hermite.h.quadrature.rules: Create list of Hermite quadrature rules In gaussquad: Collection of functions for Gaussian quadrature

## Description

This function returns a list with n elements containing the order n quadrature rule data frame for the Hermite polynomials for orders k = 1,\;2,\; … ,\;n.

## Usage

 `1` ```hermite.h.quadrature.rules(n,normalized=FALSE) ```

## Arguments

 `n` integer highest order `normalized` boolean value. if TRUE rules are for orthonormal polynomials, otherwise they are for orthgonal polynomials

## Details

An order k quadrature data frame is a named data frame that contains the roots and abscissa values of the corresponding order k orthogonal polynomial. The column with name `x` contains the roots or zeros and the column with name `w` contains the weights.

## Value

A list with n elements each of which is a data frame

 `1 ` Quadrature rule data frame for the order 1 Hermite polynomial `2 ` Quadrature rule data frame for the order 2 Hermite polynomial

...

 `n ` Quadrature rule data frame for the order n Hermite polynomial

## 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.

## See Also

`quadrature.rules`, `hermite.h.quadrature`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```### ### generate the list of quadrature rules for ### the Hermite orthogonal polynomials ### of orders 1 to 5 ### orthogonal.rules <- hermite.h.quadrature.rules( 5 ) print( orthogonal.rules ) ### ### generate the list of quadrature rules for ### the Hermite orthonormal polynomials ### of orders 1 to 5 ### orthonormal.rules <- hermite.h.quadrature.rules( 5, TRUE ) print( orthonormal.rules ) ```

gaussquad documentation built on May 30, 2017, 8:06 a.m.