Results 1 to 10 of about 588 (212)
On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials [PDF]
Journal of Classical Analysis, 2021 Summary: In this paper, we present new results on the location of zeros of some classes of quasiorthogonal polynomials. From the Chebyshev polynomials, we obtain some classes of real selfreciprocal polynomials, and investigate the location and monotonicity of their zeros.
Botta, Vanessa, Suni, Mijael Hancco
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Location of zeros Part I: Real polynomials and entire functions [PDF]
Illinois Journal of Mathematics, 1983 In the study of the distribution of zeros of polynomials and entire functions the techniques used, roughly speaking, fall into three categories" analytic, geometric and algebraic. In this paper, which represents the first portion of a two-part investigation, we will attempt to exploit the advantages of all three techniques.
Craven, Thomas, Csordas, George
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Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality
Journal of Approximation Theory, 2001 The following problem is investigated: let \(f\) be a polynomial given by the expansion \(f(z)=a_0 p_0(z)+a_1p_1(z)+\cdots+a_np_n(z)\) in terms of orthogonal polynomials. What can be said about the zeros of \(f\) in terms of the zeros of the orthogonal polynomials \(p_j\) and the Fourier coefficients \(a_j\)? The main result is a condition on the (real)
G. Schmeisser
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Mathematics, 2021 Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations,
C. Ryoo, J. Kang
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AppliedMath, 2023 Motivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and give bounds on the
Robert Gardner, M. Gladin
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q-Eulerian Polynomials and Polynomials with Only Real Zeros [PDF]
Electronic Journal of Combinatorics, 2006 Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the results of ...
Shi-Mei Ma, Yi Wang
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Number of Zeros of a Polynomial in a Specific Region with Restricted Coefficients
Journal of Mathematics and Applications, 2019 This paper focuses on the problem concerning the location and the number of zeros of polynomials in a specific region when their coefficients are restricted with special conditions.
A. Mir, Abrar Ahmad, A. Malik
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On Freud–Sobolev type orthogonal polynomials [PDF]
Afrika Matematika, 2017 In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product $$\begin{aligned} \left\langle p,q\right\rangle _{1}=\int _{\mathbb {R}}p(x)q(x)e^{-x^{4}}dx+M_{0}p(0)q(0)+M_{1}p^{\prime }(0)
L. Garza +2 more
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Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures
, 2010 Zeros of orthogonal polynomials associated with two different Sobolev inner products involving the Jacobi measure are studied. In particular, each of these Sobolev inner products involves a pair of closely related Jacobi measures.
E. Andrade +3 more
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The zeros of certain composite polynomials
, 1943 we may obtain various theorems on the relative location of the zeros of A 0(2) and An(z) by the familiar method of first finding such relations for two successive Ak{z) and then iterating the relations n times.
M. Marden
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