Results 11 to 20 of about 828 (215)
On Determinant Expansions for Hankel Operators [PDF]
Concrete Operators, 2020 Let w be a semiclassical weight that is generic in Magnus’s sense, and (pn)n=0∞({p_n})_{n = 0}^\infty the corresponding sequence of orthogonal polynomials. We express the Christoffel–Darboux kernel as a sum of products of Hankel integral operators.
Blower Gordon, Chen Yang
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Painlevé III′ and the Hankel determinant generated by a singularly perturbed Gaussian weight
Nuclear Physics B, 2018 In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weightw(x,t)=e−x2−tx2,x∈(−∞,∞),t>0. By using the ladder operator approach associated with the orthogonal polynomials, we show that the logarithmic derivative of ...
Chao Min, Shulin Lyu, Yang Chen
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The Second Hankel Determinant Problem for a Class of Bi-Univalent Functions
Journal of Mathematical and Fundamental Sciences, 2019 Hankel matrices are related to a wide range of disparate determinant computations and algorithms and some very attractive computational properties are allocated to them.
Mohammad Hasan Khani +2 more
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Evaluation of a Special Hankel Determinant of Binomial Coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 This paper makes use of the recently introduced technique of $\gamma$-operators to evaluate the Hankel determinant with binomial coefficient entries $a_k = (3 k)! / (2k)! k!$. We actually evaluate the determinant of a class of polynomials $a_k(x)$ having
Ömer Eugeciouglu +2 more
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Fractal and Fractional, 2022 This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant H3(1) for this subclass by applying the Carlson–Shaffer operator to it.
Najeeb Ullah +5 more
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What is a vector Hankel determinant
Linear Algebra and its Applications, 1998 The aim of the paper under review is to give, under some assumptions, a necessary and sufficient condition that the following system \[ \sum_{j=1}^n x_j a_{i,j} = b_i, \] where \(i=1,\dots,n\), and the \(a_{i,j}\)'s and the \(b_i\)'s are in a euclidean vector space \(V\) of dimension \(n\), has one and only one solution.
Salam, A.
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Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions [PDF]
Abstract and Applied Analysis, 2014 In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant |a2a4−a32| for functions belonging to the subclasses S(α,β),
Ming-Sheng Liu, Jun-Feng Xu, Ming Yang
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Journal of Inequalities and ApplicationsMaking use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized biunivalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel
Pishtiwan Othman Sabir +5 more
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Perturbed Hankel determinants [PDF]
Journal of Physics A: Mathematical and General, 2005 10 ...
Basor, Estelle, Chen, Yang
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Second Hankel Determinant for Analytic Functions Defined by Ruscheweyh Derivative
International Journal of Analysis and Applications, 2015 Let S denote the class of analytic and univalent functions in the open unit disk D= {z:|z|<1} with the normalization conditions. In the present article an upper bound for the second Hankel determinant |a₂a₄-a₃²| is obtained for the analytic functions ...
T. Yavuz
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