Results 61 to 70 of about 3,034 (119)

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, Luc Vinet, Alexei Zhedanov   +2 more
wiley   +1 more source

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

, 2012
Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator.
Abramowitz M, Andrews G E, Beltrami E, Bers L, Byrd P F, Cohl H S, Cohl H S, Cohl H S, E G Kalnins, Erdélyi A, Erdélyi A, Fano U, Folland G B, Fox L, Gilbarg D, Gradshteyn I S, Grigor’yan A A, Grigor’yan A A, Grigor’yan A A, H S Cohl, Helgason S, Izmest’ev A A, Kalnins E G, Lee J M, Livio M, Losev A G, Magnus W, Morse P M, Olevskii˘ M N, Olver F W J, Olver F W J, Schoen R, Thurston W P, Trudeau R J, Vilenkin N Ja   +34 more
core   +2 more sources

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

On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative

Journal of Inequalities and Applications
In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the
Yanru Wu, Monireh Nosrati Sahlan, Hojjat Afshari, Maryam Atapour, Ardashir Mohammadzadeh   +4 more
doaj   +1 more source

A probabilistic interpretation of a sequence related to Narayana polynomials [PDF]

, 2012
A sequence of coefficients appearing in a recurrence for the Narayana polynomials is generalized. The coefficients are given a probabilistic interpretation in terms of beta distributed random variables. The recurrence established by M.
Amdeberhan, T., Moll, V. H., Vignat, C.
core   +1 more source

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Annalen der Physik, Volume 536, Issue 3, March 2024.
A novel approach to quantum coupling is introduced, departing from the conventional potential‐based interaction in standard quantum mechanics. Within this framework, a quantum coupling emerges from the inherent kinetic energy of particles. This unorthodox coupling results in the transformation of quantum mechanics' fundamental landscape through the ...
Tomer Shushi
wiley   +1 more source

A Convergent Legendre Spectral Collocation Method for the Variable‐Order Fractional‐Functional Optimal Control Problems

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, a numerical method is applied to approximate the solution of variable‐order fractional‐functional optimal control problems. The variable‐order fractional derivative is described in the type III Caputo sense. The technique of approximating the optimal solution of the problem using Lagrange interpolating polynomials is employed by ...
Zahra Pirouzeh, Mohammad Hadi Noori Skandari, Kameleh Nassiri Pirbazari, Ammar Alsinai   +3 more
wiley   +1 more source

From Fourier to Gegenbauer: Dimension walks on spheres [PDF]

, 2014
We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we give closed form
Fiedler, Jochen
core  

Some Generating Functions of Modified Gegenbauer Polynomials by Lie Algebraic Method

Mathematics and Statistics, 2014
In this paper we have obtained some novel generating functions of C + n n (x)-a modification of Gegenbauer polynomials, C n (x) by utilizing L. Wesiner's group-theoretic method. By giving suitable interpretations to both the index (n) and the parameter () of the polynomial under consideration, we obtain, in section 2, a set of infinitesimal operators ...
K.P. Samanta, B. C. Chandra, C.S. Bera
openaire   +1 more source

Initial Coefficient Estimates for Bi‐Univalent Functions Related to Generalized Telephone Numbers

Journal of Mathematics, Volume 2024, Issue 1, 2024.
This study defines three novel classes of bi‐univalent functions connected to generalized telephone numbers for the first time. We produced assessments about the Taylor–Maclaurin coefficients |a2| and |a3| and Fekete–Szegö functional problems for functions involving these novel subclasses for functions in every one regarding these three bi‐univalent ...
Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, Sunil Dutt Purohit, Shyamsunder, Daya Lal Suthar, Ming-Sheng Liu   +5 more
wiley   +1 more source