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Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight
Nuclear Physics B, 2020 We study the Hankel determinant generated by a singularly perturbed Jacobi weightw(x,t):=(1−x2)αe−tx2,x∈[−1,1],α>0,t≥0. If t=0, it is reduced to the classical symmetric Jacobi weight.
Chao Min, Yang Chen
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Axioms, 2022 The logarithmic coefficients are very essential in the problems of univalent functions theory. The importance of the logarithmic coefficients is due to the fact that the bounds on logarithmic coefficients of f can transfer to the Taylor coefficients of ...
Sevtap Sümer Eker +3 more
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Hankel continued fractions and Hankel determinants of the Euler numbers [PDF]
Transactions of the American Mathematical Society, 2020 The Euler numbers occur in the Taylor expansion of tan (
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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 ...
Cigler, Johann, Tyson, Mike
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Hankel Determinants of Zeta Values [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 We study the asymptotics of Hankel determinants constructed using the values $ζ(an+b)$ of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.
Haynes, Alan, Zudilin, Wadim
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Almost Product Evaluation of Hankel Determinants [PDF]
The Electronic Journal of Combinatorics, 2008 An extensive literature exists describing various techniques for the evaluation of Hankel determinants. The prevailing methods such as Dodgson condensation, continued fraction expansion, LU decomposition, all produce product formulas when they are applicable.
Ömer Egecioglu +2 more
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Determinants of Hankel Matrices
Journal of Functional Analysis, 2001 18 pages, LaTeX ...
Basor, Estelle L. +2 more
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Evaluation of some Hankel determinants
Advances in Applied Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hou, Q.-H., Lascoux, Alain, Mu, Y.-P.
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Bounds for the second Hankel determinant of certain univalent functions [PDF]
, 2016 The estimates for the second Hankel determinant a_2 a_4-a_3^2 of the analytic function f(z)=z+a_2 z^2+a_3 z^3+⋯, for which either zf^' (z)/f(z) or 1+zf^'' (z)/f^' (z) is subordinate to a certain analytic function, are investigated.
Liew, P. H, Aini Janteng, Fuah, K. H
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The kissing polynomials and their Hankel determinants [PDF]
Transactions of Mathematics and Its Applications, 2021 AbstractIn this paper, we investigate algebraic, differential and asymptotic properties of polynomials $p_n(x)$ that are orthogonal with respect to the complex oscillatory weight $w(x)=\mathrm {e}^{\mathrm {i}\omega x}$ on the interval $[-1,1]$, where $\omega>0$.
Celsus, Andrew +3 more
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