# jacobi.g.quadrature.rules: Create list of Jacobi quadrature rules In gaussquad: Collection of functions for Gaussian quadrature

## Description

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

## Usage

 `1` ```jacobi.g.quadrature.rules(n,p,q,normalized=FALSE) ```

## Arguments

 `n` integer value for the highest order `p` numeric value for the first polynomial parameter `q` numeric value for the second polynomial parameter `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 Jacobi polynomial `2 ` Quadrature rule data frame for the order 2 Jacobi polynomial

...

 `n ` Quadrature rule data frame for the order n Jacobi 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.

`quadrature.rules`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```### ### generate the list of quadrature rule data frames for ### the orthogonal Jacobi G polynomial ### of orders 1 to 5 ### parameter p is 3 and parameter q is 2 ### orthogonal.rules <- jacobi.g.quadrature.rules( 5, 3, 2 ) print( orthogonal.rules ) ### ### generate the list of quadrature rule data frames for ### the orthonormal Jacobi G polynomial ### of orders 1 to 5 ### parameter p is 3 and parameter q is 2 ### orthonormal.rules <- jacobi.g.quadrature.rules( 5, 3, 2, TRUE ) print( orthonormal.rules ) ```