Results 91 to 100 of about 446,531 (268)

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., Gradshteyn I. S., Jan Möllers, Toshiyuki Kobayashi   +3 more
core   +1 more source

An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials [PDF]

, 2022
Ala Amourah, Basem Aref Frasin, T. M. Seoudy   +2 more
openalex   +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  

On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

International Journal of Mathematics and Mathematical Sciences, 2009
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2.
Tian-Xiao He, Peter J.-S. Shiue
doaj   +1 more source

Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

Advances in Difference Equations, 2019
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Dojin Kim   +3 more
doaj   +1 more source

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

On Mittag-Leffler-Gegenbauer polynomials arising by the convolution of Mittag-Leffler function and Hermite polynomials

AIMS Mathematics
Gegenbauer polynomials hold a significant role in the constructive theory of spherical functions, while the Mittag-Leffler function is widely used in fractional calculus.
Mohra Zayed, Maged G. Bin-Saad, Waleed K. Mohammed   +2 more
doaj   +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, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +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

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