Results 51 to 60 of about 8,276 (242)

The kissing polynomials and their Hankel determinants [PDF]

, 2016
We study a family of polynomials that are orthogonal with respect to the weight function $e^{i\omega x}$ in $[-1,1]$, where $\omega\geq 0$. Since this weight function is complex-valued and, for large $\omega$, highly oscillatory, many results in the ...
Celsius, Andrew F., Deaño Cabrera, Alfredo, Huybrechs, Daan, Iserles, Arieh   +3 more
core   +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

On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f(0) = f′(0)−1 = 0, associated with exponential functions.
Breaz Daniel, Cătaş Adriana, Cotîrlă Luminiţa-Ioana   +2 more
doaj   +1 more source

Universally prestarlike functions associated with shell like domain

Математичні Студії, 2022
In this paper, we introduce universally prestarlike generalized functions of order $\vartheta $ with $\vartheta \leq 1$ associated with shell like domain, and we get coefficient bounds and the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for such ...
K. Vijaya, G. Murugusundaramoorthy, S. Yalçın   +2 more
doaj   +1 more source

On $t$-extensions of the Hankel determinants of certain automatic sequences

, 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
core   +1 more source

On determinants identity minus Hankel matrix [PDF]

Bulletin of the London Mathematical Society, 2019
In this note, we study the asymptotics of the determinant $\det(I_N - H_N)$ for $N$ large, where $H_N$ is the $N\times N$ restriction of a Hankel matrix $H$ with finitely many jump discontinuities in its symbol satisfying $\|H\|\leq 1$. Moreover, we assume $ \in\mathbb C$ with $| |<1$ and $I_N$ denotes the identity matrix. We determine the first
Fedele, Emilio, Gebert, Martin
openaire   +2 more sources

A remark on the Hankel determinant formula for solutions of the Toda equation

, 2007
We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in ...
Fadeev L D, Goto H, Hirota R, Iwasaki K, Jimbo M, Joshi N, Kajiwara K, Kenji Kajiwara, Marta Mazzocco, Miwa T, Miwa T, Moser J, Noumi M, Okamoto K, Okamoto K, Okamoto K, Okamoto K, Ueno K, Yasuhiro Ohta   +18 more
core   +2 more sources

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.
Wen, Zhi-xiong, Wu, Wen
openaire   +2 more sources

Fiber Bragg Gratings with Micro‐Engineered Temperature Coefficients

Advanced Optical Materials, Volume 13, Issue 8, March 13, 2025.
Fiber Bragg gratings (FBGs) are intrinsically responsive to temperature and strain simultaneously. In this research, low‐loss FBGs with micro‐engineered temperature coefficients are fabricated, utilizing refractive index liquid‐filled microchannels in the cladding.
Zipei Song, Mohan Wang, Frank P. Payne, Patrick S. Salter, Tongyu Liu, Steve J. Elston, Martin J. Booth, Stephen M. Morris, Julian A. J. Fells   +8 more
wiley   +1 more source

Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions ...
Deekonda Vamshee Krishna, Nallamothu Vani, Biswajit Rath, Karri Sanjay Kumar   +3 more
doaj   +1 more source