Results 71 to 80 of about 2,224 (227)
The K Extended Laguerre Polynomials Involving Aαr,n,kxFr r,r>2
Advances in Mathematical Physics, 2022 In this manuscript, we present the generalized hypergeometric function of the type Fr r,r>2 and extension of the K Laguerre polynomial for the K extended Laguerre polynomials Ar,n,kαx.
Adnan Khan +3 more
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Singular Electromagnetics: From Phase Singularities to Optical Skyrmions and Beyond
Advanced Physics Research, Volume 4, Issue 5, May 2025.Singular electromagnetics/optics studies multidimensional topological defects of electromagnetic fields (also known as optical singularities), including phase and polarization singularities, 3D singularities (e.g., optical skyrmions, merons, hopfions, knots, links, and Möbius strips), and even higher‐dimensional singularities.
Jie Yang +3 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
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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
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Polynomials of the Laguerre type
Filomat, 2012 In this noteweshall study a class of polynomials {f c,r n,m(x)}, where c is some real number, r ? N?{0}, m ? N. These polynomials are defined by the generating function. Also, for these polynomials we find an explicit representation in the form of the hypergeometric function; some identities of the convolution type are presented; some ...
openaire +3 more sources
Laguerre derivative and monogenic Laguerre polynomials: An operational approach
Mathematical and Computer Modelling, 2011 Hypercomplex function theory generalizes the theory of holomorphic functions of one complex variable by using Clifford Algebras and provides the fundamentals of Clifford Analysis as a refinement of Harmonic Analysis in higher dimensions. We define the Laguerre derivative operator in hypercomplex context and by using operational techniques we construct ...
Cação, I. +2 more
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Structured Light Fields with 2D Tunable Indices Generated in a Raman Microchip Laser
Advanced Physics Research, Volume 4, Issue 5, May 2025.HGm,n modes with 2D tunable indices of m up to 14 and n up to 2 oscillated in a highly efficient Yb:YAG/YVO4 Raman microchip laser pumped with a rectangular beam with a suitable ratio of wx/wy. High‐order LGp,l optical vortices with 2D tunable radial index p up to 2, and azimuthal index up to 14 are converted with an astigmatic mode convertor ...
Ye Zhang +5 more
wiley +1 more source
Advantage of Non‐Gaussian Operations in Phase Estimation via Mach–Zehnder Interferometer
Advanced Quantum Technologies, Volume 8, Issue 5, May 2025.This research delves into the advantages rendered by probabilistic non‐Gaussian operations in phase estimation, using Mach–Zehnder interferometers with difference‐intensity and parity detection measurement schemes. An experimentally viable scheme is considered to implement three distinct non‐Gaussian operations, namely, photon subtraction, photon ...
Manali Verma +3 more
wiley +1 more source
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 +3 more
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DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER WITH ORTHOGONAL POLYNOMIAL SOLUTIONS
Pesquimat, 2014 In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients.
Santiago César Rojas Romero
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