orthopolynom (version 1.0-6.1)

monic.polynomials: Create list of monic orthogonal polynomials

Description

This function returns a list with \(n + 1\) elements containing the order \(k\) monic polynomials for orders \(k = 0,\;1,\; \ldots ,\;n\).

Usage

monic.polynomials(monic.recurrences)

Value

A list with \(n + 1\) polynomial objects

1

order 0 monic orthogonal polynomial

2

order 1 monic orthogonal polynomial

...

n+1

order \(n\) monic orthogonal polynomial

Arguments

monic.recurrences

a data frame containing the parameters a and b

Author

Frederick Novomestky

References

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.

See Also

monic.polynomial.recurrences

Examples

###
### generate the recurrences for the T Chebyshev polynomials
### of orders 0 to 10
###
r <- chebyshev.t.recurrences( 10, normalized=TRUE )
###
### get the corresponding monic polynomial recurrences
###
m.r <- monic.polynomial.recurrences( r )
###
### obtain the list of monic polynomials
###
p.list <- monic.polynomials( m.r )