An irreducible polynomial is polynomial that cannot be written as a product of nontrivial polynomials over the same field.
A root of a polynomial P is an element r[member of] K so that P(r) = 0, where P(r) = [a.sub.0] + [a.sub.1]*r + [a.sub.2]*[r.sup.2] + ...
The outline of this paper is as follows: in Section 2 we review many standard properties of general orthogonal polynomial systems that are exploited for computing induced distributions.
The authors in [11] proposed sampling from an additive mixture of induced distributions using a Markov Chain Monte Carlo method for the purposes of computing polynomial approximations of functions via discrete least-squares; the work in [19] investigates sampling from the n-asymptotic limit of these additive mixtures.
The standard pseudospectral method was utilized in [7] to prove new properties of the zeros of Krall polynomials. While Krall polynomials are eigenfunctions of linear differential operators, the polynomial families considered in this paper satisfy differential equations (1) with [q.sub.n](x) being polynomials (as opposed to eigenvalues) of degree [n.sub.0], where [n.sub.0] does not depend on n.
The Orthogonal Polynomial Family [{[p.sub.v](x)}.sup.[infinity].sub.v=0].
For the class of polynomials having no zero in [absolute value of z] < 1, Lax [2] proved that if p(z) is a polynomial of degree n having no zero in [absolute value of z] < 1, then
On the other hand, Turan [3] showed that, for a polynomial having all its zeros in [absolute value of z] [less than or equal to] 1,
which corresponds to the q-analog of the generating function defined in (1) and with this, new research emerged about other polynomial families based on the q-analogs.
[11] introduced a class the polynomials [B.sup.[m-1].sub.n] (x), considering a class of Appell polynomials defined by using a generating function linked to the Mittag-Leffler function (see, [12, p.
In this section, we solve ordinary and partial differential equations by ADM based on Bernstein polynomials and we compare with ADM based on classical Bernstein polynomial.
Figure 1 presents the absolute error of ADM with Bernstein polynomial in (a) and ADM with modified Bernstein polynomial in (b) at m=v=6 and k=2.
Until now, methods with trend item removal have usually employed polynomial fitting and EMD.
When the EMD and polynomial fitting methods are used to remove a vibration signal trend item, there is usually a large error at the start and the end of the signal [26].
