Results 51 to 60 of about 700 (183)

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

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

Monotonicity of zeros of Laguerre polynomials

Journal of Computational and Applied Mathematics, 2009
Monotonicity, with respect to a parameter, of certain functions involving the zeros \(x_{nk}(\alpha)\) of the Laguerre polynomial \(L_n^{(\alpha)}(x)\) is studied. It is assumed that the zeros are arranged in decreasing order and it is proved that for any \( n \geq 2\) and \(k=1,\dots,n\), the quantities \[ \frac{x_{nk}(\alpha)-(2n+\alpha-1)}{\sqrt{2(n+
Dimitar K. Dimitrov 0001, Fernando R. Rafaeli   +1 more
openaire   +2 more sources

Direct Photocurrent Detection of Optical Vortex Based on the Orbital Photo Galvanic Effect: Progress, Challenge, and Perspective

Advanced Science, Volume 13, Issue 27, 13 May 2026.
Direct orbital angular momentum (OAM) detection through the orbital photogalvanic effect offers a scalable route for integrated optoelectronics. This perspective evaluates symmetry‐driven material selection and demonstrates how electrode matrices enable the resolution of complex, mixed OAM modes.
Jinluo Cheng, Dehong Yang, Weiming Wang, Chang Xu, Zipu Fan, Dong Sun   +5 more
wiley   +1 more source

Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials

Abstract and Applied Analysis, 2012
Let Pn={p(x)∈ℝ[x]∣deg  p(x)≤n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x),q(x)∈Pn and α∈ℝ with α>-1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis
Taekyun Kim, Dae San Kim
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

The Combinatorics of Associated Laguerre Polynomials [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2015
The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.
Kim, J.S., Stanton, D.
openaire   +4 more sources

Countable Basis for Free Electromagnetic Fields

Annalen der Physik, Volume 538, Issue 5, May 2026.
ABSTRACT Polychromatic electromagnetic fields are expanded as integrals over monochromatic fields, such as plane waves, multipolar fields, or Bessel beams. However, monochromatic fields do not belong to the Hilbert space of free Maxwell fields, since their norms diverge.
Ivan Fernandez‐Corbaton
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

Fractional Orbital Angular Momentum Sorting Using Wind Spiral Transformation

Nanophotonics, Volume 15, Issue 8, 24 April 2026.
A wind‐spiral coordinate transformation enables mode sorting of fractional‐order orbital angular momentum (OAM) states, overcoming the limited channel count of conventional integer only sorters. Fractional OAM is mapped into a controlled superposition of integer modes, producing distinctive multi‐peak signatures for discrimination.
Xiaobin Yang, Mengran Fan, Hao Zhang, Kun Liu, Juntao Hu, Yuping Tai, Yijie Shen, Xinzhong Li   +7 more
wiley   +1 more source