Results 11 to 20 of about 8,275 (212)
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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On $t$-extensions of the Hankel determinants of certain automatic sequences
Theoretical Computer Science, 2014 In 1998, Allouche, Peyri\`ere, Wen and Wen considered the Thue--Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integral numbers.
Fu, Hao, Han, Guo-Niu
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Hankel determinants and Bernoulli numbers [PDF]
Tohoku Mathematical Journal, 1954 L. Carlitz
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Hankel determinant for a class of analytic functions [PDF]
, 2019 Let $f$ be analutic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bound of Hankel determinant of the second order for the class of analytic unctions satisfying \[ \left|\arg \left[\left ...
Obradovic, Milutin, Tuneski, Nikola
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Evaluation of some Hankel determinants
Advances in Applied Mathematics, 2005 AbstractWe evaluate some Hankel determinants of Meixner polynomials, associated to the series exp(∑α[i]zi/i), where [1],[2],… are the q-integers.
Qing-Hu Hou, Alain Lascoux, Yan-Ping Mu
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Hankel determinants of Eisenstein series [PDF]
, 2000 In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $ $ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants for $E_{2r} ^m$, for $m=1,2,3$ and $r=2,3,4,5,7$, and $E_{14} ^4$.
Stephen C. Milne
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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 $ (an+b)$ of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.
Alan Haynes, Wadim Zudilin
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Hankel determinants for some common lattice paths [PDF]
Advances in Applied Mathematics, 2007 For a single value of $\ell$, let $f(n,\ell)$ denote the number of lattice paths that use the steps $(1,1)$, $(1,-1)$, and $(\ell,0)$, that run from $(0,0)$ to $(n,0)$, and that never run below the horizontal axis. Equivalently, $f(n,\ell)$ satisfies the quadratic functional equation $F(x) = \sum_{n\ge 0}f(n,\ell) x^n = 1+x^{\ell}F(x)+x^2F(x)^2.$ Let ...
Robert A. Sulanke, Guoce Xin
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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 $\omega>0$.
Celsius, Andrew F. +3 more
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Proof of the Somos-4 Hankel determinants conjecture [PDF]
Advances in Applied Mathematics, 2008 3 ...
Guoce Xin
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