Nothing
chebyshev.s.recurrences <- function( n, normalized=FALSE )
{
###
### This function returns a data frame with n+1 rows and four columns
### containing the coefficients c, d, e and f of the recurrence relations
### for the order k Chebyshev polynomial of the second kind, Sk(x),
### and for orders k=0,1,...,n
###
### Parameter
### n = integer highest order
### normalized = boolean value. If true, recurrences are for normalized polynomials
###
if ( n < 0 )
stop( "negative highest polynomial order" )
if ( n != round( n ) )
stop( "highest polynomial order is not integer" )
np1 <- n + 1
r <- data.frame( matrix( nrow=np1, ncol=4 ) )
names( r ) <- c( "c", "d", "e", "f" )
j <- 0
k <- 1
if ( normalized ) {
while ( j <= n ) {
r[k,"c"] <- 1
r[k,"d"] <- 0
r[k,"e"] <- 1
if ( j == 0 )
r[k,"f"] <- 0
else {
r[k,"f"] <- 1
}
j <- j + 1
k <- k + 1
}
return( r )
}
else {
r$c <- rep( 1, np1 )
r$d <- rep( 0, np1 )
r$e <- rep( 1, np1 )
r$f <- rep( 1, np1 )
return( r )
}
return( NULL )
}
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