Create list of Legendre 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 Legendre polynomial for orders k = 1,\;2,\; … ,\;n.

Usage

1

Arguments

n

integer value for the 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 Legendre polynomial

2

Quadrature rule data frame for the order 2 Legendre polynomial

...

n

Quadrature rule data frame for the order $n$ Legendre polynomial

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Abramowitz and Stegun (1968), Press et. al. (1992)

See Also

quadrature.rules

Examples

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###
### generate a list of quadrature rule frames for
### the orthogonal Legendre polynomials
### of orders 1 to 5
###
orthogonal.rules <- legendre.quadrature.rules( 5 )
print( orthogonal.rules )
###
### generate a list of quadrature rule frames for
### the orthonormal Legendre polynomials
### of orders 1 to 5
###
orthonormal.rules <- legendre.quadrature.rules( 5, TRUE )
print( orthonormal.rules )

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