Nothing
jacobi.g.inner.products <- function( n, p, q )
{
###
### This function returns a vector with n+1 elements
### containing the inner product of an order k Jacobi polynomial
### Gk(p,q,x) with itself (i.e. norm squared) for orders k=0,1,...,n
###
### Parameters
### n = integer highest polynomial order
### p = first parameter
### q = second parameter
###
if ( n < 0 )
stop( "negative highest polynomial order" )
if ( n != round( n ) )
stop( "highest polynomial order is not integer" )
if ( ( p - q ) <= -1 )
stop( "p minus q less than or equal to -1" )
if ( q <= 0 )
stop( "q less than or equal to 0" )
inner.products <- rep( 1, n + 1 )
pmq <- p - q
inner.products[1] <- gamma( q ) * gamma( pmq + 1 ) / gamma( p + 1 )
j <- 2
for ( k in 1:n ) {
num <- factorial( k ) * gamma( k + q ) * gamma( k + p ) * gamma( k + pmq + 1 )
den <- ( 2 * k + p ) * ( gamma( 2 * k + p ) ^ 2 )
inner.products[j] <- num / den
j <- j + 1
}
return( inner.products )
}
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