legpolypow
Power of Legendre polynoamials.
Syntax
f = legpolypow(p, n, order4trunc)
Description
f = legpolypow(p, n) is a recursive application of chebypolyprod
funtion, computing sum(p_i*T_i)^n. i.e. If
P(x) = p(1)*L_0(x) + ... + p(m+1)*L_m(x),
then the result will be the vector of coefficients y such that
P(x)^n = f(1)*L_0(x) + ... + f(m+n+1)*L_{m+n+1}(x).
Inputs
p = vector of coefficients in Legendre basis.
n = power degree.
Output
f = vector of coefficients in Legendre basis (P(x)^n).
Example
legpolyprod(legpolyprod(legpolyprod( ...
[1 2 3], [1 2 3]), [1 2 3]), [1 2 3]) - legpolypow([1 2 3], 4)
The result must be zeros.
f = legpolypow(p, n) is a recursive application of chebypolyprod
funtion, computing sum(p_i*T_i)^n. i.e. If
P(x) = p(1)*L_0(x) + ... + p(m+1)*L_m(x),
then the result will be the vector of coefficients y such that
P(x)^n = f(1)*L_0(x) + ... + f(m+n+1)*L_{m+n+1}(x).
Inputs
p = vector of coefficients in Legendre basis.
n = power degree.
Output
f = vector of coefficients in Legendre basis (P(x)^n).
Example
legpolyprod(legpolyprod(legpolyprod( ...
[1 2 3], [1 2 3]), [1 2 3]), [1 2 3]) - legpolypow([1 2 3], 4)
The result must be zeros.
f = vector of coefficients in Legendre basis (P(x)^n).