Create list of generalized Hermite quadrature rules

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Description

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

Usage

1

Arguments

n

integer value for the highest integer order

mu

numeric value for the parameter of the generalized Hermite polynomial

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 generalized Hermite polynomial

2

Quadrature rule data frame for the order 2 generalized Hermite polynomial

...

n

Quadrature rule data frame for the order n generalized Hermite polynomial

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.

See Also

quadrature.rules, schebyshev.t.quadrature

Examples

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###
### generate a list of quadrature rule data frames for
### the generalized orthogonal Hermite polynomial
### of orders 1 to 5.
### polynomial parameter mu is 1.0
###
orthogonal.rules <- ghermite.h.quadrature.rules( 5, 1 )
print( orthogonal.rules )
###
### generate a list of quadrature rule data frames for
### the generalized orthonormal Hermite polynomial
### of orders 1 to 5.
### polynomial parameter mu is 1.0
###
orthonormal.rules <- ghermite.h.quadrature.rules( 5, 1, TRUE )
print( orthonormal.rules )

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