Results 61 to 70 of about 126,262 (211)

q-Calculus as operational algebra; pp. 73–97 [PDF]

Proceedings of the Estonian Academy of Sciences, 2009
This second paper on operational calculus is a continuation of Ernst, T. q-Analogues of some operational formulas. Algebras Groups Geom., 2006, 23(4), 354–374. We find multiple q-analogues of formulas in Carlitz, L.
Thomas Ernst
doaj   +1 more source

Equioscillatory property of the Laguerre polynomials

Journal of Approximation Theory, 2010
\(L^{(\alpha)}_k\) is the orthonormal Laguerre polynomial of degree \(k\) and \(d_m\), \(d_M\) are some approximations for the extreme zeros. The authors show that the function \[ ((x- d_m)(x- d_M))^{1/4} x^{\alpha/2} e^{-{x\over 2}}L^{(\alpha)}_k(x) \] is almost equi-oscilating with the amplitude \(\sqrt{{2\over\pi}}\) provided \(k\) and \(\alpha ...
Ilia Krasikov, Alexander Zarkh
openaire   +3 more sources

A Convergent Fourier Spectral Galerkin Method for the Fractional Camassa–Holm Equation

Numerical Methods for Partial Differential Equations, Volume 42, Issue 4, July 2026.
ABSTRACT We analyze a Fourier spectral Galerkin method for the fractional Camassa–Holm (fCH) equation involving a fractional Laplacian of exponent α∈[1,2]$$ \alpha \in \left[1,2\right] $$ with periodic boundary conditions. The semi‐discrete scheme preserves both mass and energy invariants of the fCH equation.
Mukul Dwivedi, Andreas Rupp
wiley   +1 more source

On a family of q-modified-Laguerre-Appell polynomials

Arab Journal of Basic and Applied Sciences
This paper aims to introduce a new class of special polynomials called q-modified Laguerre-Appell polynomials. Some definitions and concepts related to this class of polynomials, including generating function and series definition are explored.
Mohammed Fadel, Abdulghani Muhyi
doaj   +1 more source

On Some Relations between the Hermite Polynomials and Some Well-Known Classical Polynomials and the Hypergeometric Function.

مجلة العلوم البحتة والتطبيقية, 2020
The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
doaj   +1 more source

Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions [PDF]

, 2015
We consider polynomials P_n orthogonal with respect to the weight J_? on [0,?), where J_? is the Bessel function of order ?. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals.
Deaño Cabrera, Alfredo, Kuijlaars, Arno, Kuijlaars, Arno B. J., Román, Pablo Manuel, Deaño, Alfredo, Román, Pablo   +5 more
core   +1 more source

Treeline Provides a Unified Strategy for Optimising Phylogenetic Trees Under Alternative Criteria

Molecular Ecology Resources, Volume 26, Issue 5, July 2026.
ABSTRACT The choice of optimality criterion is a key consideration in phylogenetic studies. Recent work challenges the notion that more computationally demanding optimisation objectives result in better phylogenetic trees. This finding underscores the importance of comparing trees across optimisation objectives in addition to different models of ...
Erik S. Wright
wiley   +1 more source

A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

Abstract and Applied Analysis, 2014
The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line.
Ali H. Bhrawy, Abdulrahim AlZahrani, Dumitru Baleanu, Yahia Alhamed   +3 more
doaj   +1 more source

Evolution and Conceptual Insights into the Geometric Phase of Light: A Comprehensive Review

Advanced Photonics Research, Volume 7, Issue 6, June 2026.
This review presents a unified account of the geometric phase of light, linking its fundamental principles to diverse manifestations in polarization, spatial, and vector modes. By connecting theoretical frameworks with key experimental realizations, it reveals a coherent physical picture that deepens understanding and stimulates new directions in ...
A. Srinivasa Rao
wiley   +1 more source

Extended forms of Legendre-Laguerre-based hybrid polynomials and their characteristics via fractional operator approach

Journal of Inequalities and Applications
This study presents an extensive generalization of Legendre–Laguerre polynomials along with their Appell-type counterparts. Using the quasi-monomiality approach, we establish core analytical features, including recurrence relations, associated ...
Waseem Ahmad Khan, Shahid Ahmad Wani, Mohammad Ayman-Mursaleen, Ketan Kotecha, Prakash Jadhav   +4 more
doaj   +1 more source