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Hankel Determinant Solution for Elliptic Sequence
Linear Algebra and its Applications, 2014 We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants.
Fumitaka Yura
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Hankel inequalities for bounded turning functions in the domain of cosine Hyperbolic function
AIMS Mathematics, 2023 In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning.
Muhammmad Ghaffar Khan +5 more
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Problems concerning sharp coefficient functionals of bounded turning functions
AIMS Mathematics, 2023 The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors.
Muhammmad Ghaffar Khan +3 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_{ , }].
Yang Chen, Estelle L. Basor
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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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An Interesting Class of Hankel Determinants [PDF]
, 2020 For small $r$ the Hankel determinants $d_r(n)$ of the sequence $\left({2n+r\choose n}\right)_{n\ge 0}$ are easy to guess and show an interesting modular pattern. For arbitrary $r$ and $n$ no closed formulae are known, but for each positive integer $r$ the special values $d_r(rn)$, $d_r(rn+1)$, and $d_r(rn+\lfloor\frac{r+1}{2}\rfloor)$ have nice values ...
Mike Tyson, Johann Cigler
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International Journal of Analysis and Applications, 2023 The growth of the Hankel determinant whose elements are logarithmic coefficients for different subclasses of univalent functions has recently attracted considerable interest.
Daud Mohamad +1 more
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Hankel determinants of the Cantor sequence [PDF]
SCIENTIA SINICA Mathematica, 2014 In the paper, we give the recurrent equations of the Hankel determinants of the Cantor sequence, and show that the Hankel determinants as a double sequence is 3-automatic. With the help of the Hankel determinants, we prove that the irrationality exponent of the Cantor number, i.e.
Wu Wen, Wen ZhiXiong
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Hankel determinants of a Sturmian sequence
AIMS Mathematics, 2022 <abstract><p>Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation.
Haocong Song, Wen Wu
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