Results 71 to 80 of about 5,734 (154)

Certain Constraints for Functions Provided by Touchard Polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
Since finding solutions to integral equations is usually challenging analytically, approximate methods are often required, one of which is based on Touchard polynomials. This paper examines the necessary constraints for the functions Ϝετς,Πε,τ,ςℏ, and the integral operator Lετς, defined by Touchard polynomials, to be in the comprehensive subclass ∁η(q3,
Tariq Al-Hawary, Mohamed Illafe, Feras Yousef, Shikha Binwal   +3 more
wiley   +1 more source

Momentum-space conformal blocks on the light cone

Journal of High Energy Physics, 2018
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks.
Marc Gillioz
doaj   +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

Quantum Extensions of Widder’s Formula via q‐Deformed Calculus

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In this study, we rigorously established q‐Widder’s formula of first and second kind by employing the q‐integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse q‐Laplace transform, enabling simplified computation without relying on conventional complex integration methods.
S. S. Naina Mohammed, K. Jeevanandham, A. Ramalingam, R. Maheswari, Prasantha Bharathi Dhandapani, Rebecca Muhumuza Nalule, Kaviarasan Boomipalagan   +6 more
wiley   +1 more source

Certain Relations of Gegenbauer and Modified Gegenbauer Matrix Polynomials by Lie Algebraic Method

Journal of New Theory, 2019
The object of the present paper is to derive the generating formulae for the Gegenbauer and modified Gegenbauer matrix polynomials by introducing a partial differential operatorand constructing the Lie algebra representation formalism of special linear ...
Ayman Shehata
doaj  

Radial Coordinates for Conformal Blocks

, 2013
We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is analyzed in radial quantization: individual terms describe ...
Hogervorst, Matthijs, Rychkov, Slava
core   +1 more source

Generalized Gegenbauer orthogonal polynomials

Journal of Computational and Applied Mathematics, 2001
The aim of the author is to give a characterization of the so-called generalized Gegenbauer polynomials. He first shows the link between this functions and the classical Jacobi polynomials. Then he establishes both a differential-difference and a second order differential equation satisfied by these generalized polynomials.
openaire   +2 more sources

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, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +1 more source

Old and New Identities for Bernoulli Polynomials via Fourier Series

International Journal of Mathematics and Mathematical Sciences, 2012
The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of ...
Luis M. Navas, Francisco J. Ruiz, Juan L. Varona   +2 more
doaj   +1 more source

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