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130,619
result(s) for
"Polynomials."
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RECIPROCAL MONOGENIC QUINTINOMIALS OF DEGREE $\\boldsymbol {2^n}
We prove a new irreducibility result for polynomials over
${\\mathbb Q}$
and we use it to construct new infinite families of reciprocal monogenic quintinomials in
${\\mathbb Z}[x]$
of degree
$2^n$
.
Journal Article
The connected domination polynomial of some graph constructions
The connected domination polynomial of a connected graph G of order n is the polynomial D c [ G , x ] = ∑ i = γ c n d c ( G , i ) x i , where d c ( G, i ) is the number of connected dominating sets of G of cardinality i and γ c (G) is the connected domination number of G [5]. In this paper we find the polynomial D c ( G, x ) for some constructive graphs.
Journal Article
A new generalization of bi-periodic Jacobsthal polynomials
In this paper, we have introduced a new generalization of Jacobsthal polynomial (bi-periodic Jacobsthal polynomial), have obtained Binet's formula, generating function, well-known Cassini's, Catalan's and d'Ocagne's Identities and some more results related to this polynomial.
Journal Article
A review of operational matrices and spectral techniques for fractional calculus
Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.
Journal Article
EQUATIONS WITHOUT THE POLYNOMIAL LAW: EXPLORING TWO-SERIES POSSIBILITIES
For the purpose of resolving dual series problems involving Laguerre polynomials, this essay makes use of the Noble and Lowndes multiplying factor approach.
Journal Article
IDENTITIES AND RELATIONS INVOLVING PARAMETRIC TYPE BERNOULLI
The main purpose of this paper is to give explicit relations and identities for the parametric type Bernoulli polynomials. Further, we give some relations for the generalized Bernoulli polynomials.
Journal Article
Hardy–Littlewood and Ulyanov inequalities
We give the full solution of the following problem: obtain sharp inequalities between the moduli of smoothness
The main tool is the new
Hardy–Littlewood–Nikol’skii inequalities. More precisely, we obtained the asymptotic behavior of the quantity
We also prove the
Ulyanov and Kolyada-type inequalities in the Hardy spaces. Finally, we apply the obtained estimates to derive new embedding theorems for
the Lipschitz and Besov spaces.
eBook
A Note on Degenerate Euler and Bernoulli Polynomials of Complex Variable
Recently, the so-called new type Euler polynomials have been studied without considering Euler polynomials of a complex variable. Here we study degenerate versions of these new type Euler polynomials. This has been done by considering the degenerate Euler polynomials of a complex variable. We also investigate corresponding ones for Bernoulli polynomials in the same manner. We derive some properties and identities for those new polynomials. Here we note that our result gives an affirmative answer to the question raised by the reviewer of the paper.
Journal Article