Results 41 to 50 of about 103 (90)

Orthogonal Laurent Polynomials of Two Real Variables

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT In this paper, we consider an appropriate ordering of the Laurent monomials xiyj$x^{i}y^{j}$, i,j∈Z$i,j \in \mathbb {Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables x$x$ and y$y$ with respect to a positive Borel measure μ$\mu$ defined on R2$\mathbb {R}^2$ such that ({x=0}∪{y=0})∩supp(μ)=∅$(\lbrace ...
Ruymán Cruz‐Barroso, Lidia Fernández
wiley   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source

Two-Variable q-Hermite-Based Appell Polynomials and Their Applications

Mathematics
A noteworthy advancement within the discipline of q-special function analysis involves the extension of the concept of the monomiality principle to q-special polynomials.
Mohammed Fadel, Maryam Salem Alatawi, Waseem Ahmad Khan   +2 more
doaj   +1 more source

Images for the Y‐Function via Marichev–Saigo–Maeda Fractional Integration and Differentiation Operators

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Y‐function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric‐type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y‐function, this study establishes four ...
Engdasew Birhane, D. L. Suthar, Shikha Binwal   +2 more
wiley   +1 more source

Spatially explicit predictions using spatial eigenvector maps

Methods in Ecology and Evolution, Volume 15, Issue 11, Page 2129-2140, November 2024.
Abstract In this paper, we explain how to obtain sets of descriptors of the spatial variation, which we call “predictive Moran's eigenvector maps” (pMEM), that can be used to make spatially explicit predictions for any environmental variables, biotic or abiotic. It unites features of a method called “Moran's eigenvector maps” (MEM) and those of spatial
Guillaume Guénard, Pierre Legendre
wiley   +1 more source

Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers

Mathematics
In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s-Appell polynomials related to Stirling numbers and binomial coefficients.
Tian-Xiao He, Emanuele Munarini
doaj   +1 more source

An alternative approach to averaging in nonlinear systems using classical probability density

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 104, Issue 6, June 2024.
Abstract The averaging method is a widely used technique in the field of nonlinear differential equations for effectively reducing systems with “fast” oscillations overlaying “slow” drift. The method involves calculating an integral, which can be straightforward in some cases but can also require simplifications such as series expansions. We propose an
Attila Genda, Alexander Fidlin, Oleg Gendelman   +2 more
wiley   +1 more source

A New Generalization of Two-Variable q-Gould–Hopper–Hahn–Appell Polynomials via Quantum q-Calculus

Mathematics
In this paper, we introduce a class of two-variable q-Gould–Hopper–Hahn–Appell polynomials obtained by combining a Hahn-type q-Gould–Hopper kernel with a general q-Appell factor.
Waseem Ahmad Khan, Oğuz Yağcı, Khidir Shaib Mohamed, Osman Osman, Naglaa Mohammed   +4 more
doaj   +1 more source

Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials

Studies in Applied Mathematics, Volume 152, Issue 1, Page 453-507, January 2024.
Abstract In this paper, rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalized Laguerre polynomials, which are the main subject of this paper, and the other in terms of the generalized Umemura polynomials. Both the generalized
Peter A. Clarkson, Clare Dunning
wiley   +1 more source

Expansion formulas for Apostol type \(q\)-Appell polynomials, and their special cases

Le Matematiche, 2018
Summary: We present identities of various kinds for generalized \(q\)-Apostol-Bernoulli and Apostol-Euler polynomials and power sums, which resemble \(q\)-analogues of formulas from the 2009 paper by \textit{H. M. Liu} and \textit{W. Wang} [Discrete Math. 309, No. 10, 3346--3363 (2009; Zbl 1227.11043)].
openaire   +2 more sources