Next: continfrac() Up: Mathematical Macros Help File Previous: broyden()   Contents


chebcoefs(vector(a0,a1,...,an)), a0, a1, ..., an non MISSING REAL

Keywords: expansions, power series, orthogonal polynomials
Suppose Pn(x) = a0+a1*x+ ... + an*x^n is a polynomial in x of degree
n.  Then Pn(x) has a unique expansion, Pn(x) = b0 + b1*T1(x) + ... +
bn*Tn(x), where Tj(x) = the Chebyshev polynomial of degree j defined
for -1 <= x <= 1 as Tj(x) = cos(j*acos(x)).

chebcoefs(vector(a0,a1,...,an)), where a0, a1, ..., an are non MISSING
REAL scalars returns vector(b0,b1,...,bn), where the b's are the
coefficients in the Chebyshev expansion.

See also topic invchebcoefs().

Gary Oehlert 2003-01-15