The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function [PDF]
Heliyon, 2023 In this paper, we give sharp bounds of the Hankel determinant H2(3)(f) for the coefficients of functions in the class of starlike functions related to a domain that is like three leaves.
Amina Riaz +3 more
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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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Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions [PDF]
HeliyonIn the present article, we prove the sharp upper bounds for the second order Hankel determinants |H2(1)|,|H2(2)| and related functionals |a2a3−a4|, |a2a5−a3a4| for q-starlike functions.
Ihtesham Gul +3 more
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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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Third-order Hankel determinant sharp estimates for the inverse of complex valued holomorphic functions [PDF]
HeliyonDetermining coefficient estimates of inverse complex valued function is often more challenging than determining the function itself, leading to a lack of articles on inverse functions by examining sharp estimates of the third-order Hankel determinant ...
Muhammad Abbas +3 more
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Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order [PDF]
The Scientific World Journal, 2014 The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order.
Muhammad Arif +3 more
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Sharp bounds of the third Hankel determinant for classes of univalent functions with bounded turning [PDF]
Mathematica Bohemica, 2022 We improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning.
Milutin Obradović +2 more
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Mathematics, 2023 One of the challenging tasks in the study of function theory is how to obtain sharp estimates of coefficients that appear in the Taylor–Maclaurin series of analytic univalent functions, and for obtaining these bounds, researchers used the concepts of ...
Isra Al-Shbeil +4 more
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Perturbed Hankel determinants [PDF]
Journal of Physics A: Mathematical and General, 2005 In this short note, we compute, for large n the determinant of a class of n x n Hankel matrices, which arise from a smooth perturbation of the Jacobi weight. For this purpose, we employ the same idea used in previous papers, where the unknown determinant, D_n[w_{ , }h] is compared with the known determinant D_n[w_{ , }].
Basor, Estelle, Chen, Yang
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Fourth Hankel Determinant for a Subclass of Starlike Functions Based on Modified Sigmoid
Journal of Function Spaces, 2021 In our present investigation, we obtain the improved third-order Hankel determinant for a class of starlike functions connected with modified sigmoid functions.
Wali Khan Mashwani +6 more
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