Results 1 to 10 of about 257,077 (206)
Axioms, 2023 A new subclass of bi-univalent functions associated with the Hohlov operator is introduced. Certain properties such as the coefficient bounds, Fekete-Szegö inequality and the second Hankel determinant for functions in the subclass are obtained.
Likai Liu, Jie Zhai, Jin-Lin Liu
doaj +1 more source
Hankel Determinants of Eisenstein Series [PDF]
, 2001 In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $Δ$ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants for $E_{2r}Δ^m$, for $m=1,2,3$ and $r=2,3,4,5,7$, and $E_{14}Δ^4$.
openaire +2 more sources
Hankel determinants and orthogonal polynomials
Expositiones Mathematicae, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Selberg integrals and Hankel determinants [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 In our previous works "Pfaffian decomposition and a Pfaffian analogue of $q$-Catalan Hankel determinants'' (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser. A, 120, 2013, 1263-1284) we have proposed several ways to evaluate certain Catalan-Hankel Pffafians and also formulated several conjectures.
Masao Ishikawa, Jiang Zeng
openaire +3 more sources
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
openaire +3 more sources
On Hankel and Inverse Hankel Determinants of Order Two for Some Subclasses of Analytic Functions
Symmetry, 2023 In view of the subclass SL*(β), which for β=0 reduces to the class SL*, two more subclasses CL(β) and GL(β) are introduced. For all these three subclasses, we investigate upper bounds of second Hankel and second inverse Hankel determinates. In most of the cases, the results are sharp.
Nehad Ali Shah +4 more
openaire +2 more sources
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
doaj +1 more source
Hankel determinants for some common lattice paths
Advances in Applied Mathematics, 2008 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
openaire +3 more sources
Second Hankel determinant for a class of analytic functions defined by q-derivative operator
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this paper, we obtain the estimates for the second Hankel determinant for a class of analytic functions defined by q-derivative operator and subordinate to an analytic function.
Răducanu Dorina
doaj +1 more source
Hankel determinant solution for elliptic sequence
Linear Algebra and its Applications, 2015 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.
openaire +3 more sources