polynomial

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polynomial

(pŏl′ē-nō′mē-əl)
adj.
Of, relating to, or consisting of more than two names or terms.
n.
1. A taxonomic designation consisting of more than two terms.
2. Mathematics
a. An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to nonnegative integral powers. For example, x2 - 5x + 6 and 2p3q + y are polynomials. Also called multinomial.
b. An expression of two or more terms.
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Given a fixed integer n such that 0 [less than or equal to] n [less than or equal to] N + [n.sub.0] - 1, the last identity relates the zeros of the polynomials [mathematical expression not reproducible] and [p.sub.n](x) with the zeros of all the polynomials [p.sub.j](x) such that the integer index j [member of] {0, 1, ..., N + [n.sub.0] - 1} satisfies n - [n.sub.0] [less than or equal to] j [less than or equal to] n + [n.sub.0].
We invite the reader to apply identities (60) to the Sonin-Markov polynomials, replacing [[??].sup.c] and [[??].sup.[tau]] with [[??].sup.c] and [[??].sup.[tau]], respectively, the latter being matrix representations of the differential operator D associated with the Sonin-Markov family; see (26).
Rather, "A refinement of a theorem of Paul Turaan concerning polynomials," Mathematical Inequalities and Applications, vol.
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,
The author named it the unified q-Apostol-Bernoulli, Euler, and Genocchi polynomials of order a and proved some properties for these unification.
In [18], the authors introduced the generalized q-Apostol-Bernoulli polynomials, the generalized q-Apostol Euler polynomials, and generalized q-Apostol Genocchi polynomials in variable x, y, order a, and level m through the following generating functions, defined in a suitable neighborhood of z = 0 (see, [18, p.
is called the Bernstein polynomials of degree m, where [[beta].sub.i] are the Bernstein coefficients.
where [B.sub.m](f) is the m-th Bernstein polynomials for f(x).
The degenerate Euler polynomials are defined by the generating function to be
The degenerate q-Euler polynomials are defined by the generating function to be
An irreducible polynomial is polynomial that cannot be written as a product of nontrivial polynomials over the same field.
Orthogonal polynomials. This section contains classical knowledge, most of which is available from any seminal reference on orthogonal polynomials [24, 4, 20, 6].