orthopolynom (version 1.0-2)

polynomial.powers: Create a list of polynomial linear combinations

Description

This function returns a list with $n$+1 elements containing the vector of linear combinations of the order $k$ polynomials for orders $k$ = 0, 1,..., $n$. Each element in the list is a vector.

Usage

polynomial.powers(polynomials)

Arguments

polynomials

~~Describe polynomials here~~

Value

• A list of $n$+1 elements where each element is a vector of linear combinations.
• 1
  Linear combination(s) of polynomials up to order 0
• 2
  Linear combination(s) of polynomials up to order 1
• ...
• n+1
  Linear combination(s) of polynomials up to order $n$

Details

The $j$-th component in the list is a vector of linear combinations of the order $k$ polynomials for orders $k$ = 0, 1, ..., $j-1$ equal to the monomial x raised to the power $j$-1.

Examples

polynomials <- legendre.polynomials( 10 )
alphas <- polynomial.powers( polynomials )