## chebypolypow

Power of Chebyshev polynomials.

Power of Chebyshev polynomials.

f = chebypolypow(p, n, order4trunc)

f = chebypolypow(p, n) is a recursive application of chebypolyprod funtion, to compute sum(p_i*T_i)^n. If P(x) = p(1)*T_0(x) + ... + p(m+1)*T_m(x), then the result will be the vector of coefficients y such that P(x)^n = f(1)*T_0(x) + ... + f(m+n+1)*T_{m+n+1}(x). T (Chebyshev of first kind) can be U (Chebyshev of second kind).

p = vector of coefficients in Chebyshev basis. n = power degree. order4trunc = order for truncate, if necessary.

f = vector of coefficients in Chebyshev basis (P(x)^n).

chebypolyprod(chebypolyprod(chebypolyprod( ... [1 2 3], [1 2 3]), [1 2 3]), [1 2 3]) - chebypolypow([1 2 3], 4) The result must be zeros.