e-mail: simoron@ispras.ru

**On algorithms of expansion of a given polynomial in
Boas-Buck polynomial sequences**

**Abstract**

In many applications there is a problem of finding of coefficients of
decomposition of the function on some basis, if the decomposition of this
function on other basis is known. The important examples of such problems
are funding decompositions of functions on Hermite and Laguerre polynomials.
Inthe most general the given problem is reduced to a problem of multiplying
*N
*x*N * matrices by *N*-vector. To do it is necassary
to execute *O*(*N^2*) of arithmetic operations. The representations
of transformation matrices as a product of Toeplitz and two diogonal matrices
are found for decomposition of the polynomial in Hermite and Laguerre polynomials.
It is sufficient of *O*(*N *log*N*), instead of *O*(*N^2*),
as generally.