Results 81 to 90 of about 6,252 (234)
On a Certain Class of Bi-Univalent Functions in Connection with Gegenbauer Polynomials
Pan-American Journal of MathematicsRecent direction of studies shows that there is a kin connection between regular functions and orthogonal polynomials. In this paper, we study a new class of regular and bi-univalent functions that involve the familiar Gegenbauer polynomials.
Rasheed Olawale Ayinla +1 more
doaj +1 more source
An integral formula for L^2-eigenfunctions of a fourth order Bessel-type differential operator
, 2010 We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions.
Erdélyi A. +3 more
core +1 more source
Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers
Journal of Mathematics, Volume 2025, Issue 1, 2025.Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di +3 more
wiley +1 more source
A four dimensional Bernstein Theorem
, 2019 We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result in terms of ...
Perotti, Alessandro
core
Continuous −1$-1$ hypergeometric orthogonal polynomials
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier +2 more
wiley +1 more source
Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials
Mathematics, 2019 The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method.
Harendra Singh +2 more
doaj +1 more source
Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials
Mathematics, 2020 In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and ...
Taekyun Kim +3 more
doaj +1 more source
A note on the squarefree density of polynomials
Mathematika, Volume 70, Issue 4, October 2024.Abstract The conjectured squarefree density of an integral polynomial P$\mathcal {P}$ in s$s$ variables is an Euler product SP$\mathfrak {S}_{\mathcal {P}}$ which can be considered as a product of local densities. We show that a necessary and sufficient condition for SP$\mathfrak {S}_{\mathcal {P}}$ to be 0 when P∈Z(X1,…,Xs)$\mathcal {P}\in \mathbb {Z}(
R. C. Vaughan, Yu. G. Zarhin
wiley +1 more source
Noise‐Tailored Constructions for Spin Wigner Function Kernels
Advanced Physics Research, Volume 3, Issue 6, June 2024.This work explores the parameterization of spin Wigner functions to efficiently represent the effects of probabilistic unitary noise on a quantum state. Block diagonalization of the noise operator algebra is used to reduce the required number of parameters while maintaining the Stratonovich–Weyl conditions for the representation.
Michael Hanks, Soovin Lee, M.S. Kim
wiley +1 more source
Matrix-valued Gegenbauer polynomials
, 2014 25 pages, accompanying Maple worksheet available at http://www.math.ru.nl/~koelink/publist-ro.html. Proofs have been simplified by exploiting shift operators extensively. The proofs of the symmetry of some matrix-valued differential operators have been simplified using the LDU-decomposition of the weight. The proof of the matrix-valued Pearson equation
Koelink, Erik +2 more
openaire +2 more sources