Results 71 to 80 of about 5,765 (234)

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

Investigating the Properties and Dynamic Applications of Δ_h Legendre–Appell Polynomials

Mathematics
This research aims to introduce and examine a new type of polynomial called the Δh Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δh Legendre–Appell polynomials and explore their properties.
Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Hasan Nihal Zaidi   +3 more
doaj   +1 more source

Coordinating representation registers: linear algebra students' understanding of orthogonal Legendre polynomials in the inner product space ℙn in a technology-assisted learning environment

Annales de Didactique et de Sciences Cognitives, 2018
The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of the orthogonal Legendre polynomials as vectors of the inner product space ℙn in a DGS (Dynamic Geometry Software)-MATLAB ...
Günhan Caglayan
doaj   +1 more source

Accurate Evaluation of Polynomials in Legendre Basis [PDF]

Journal of Applied Mathematics, 2014
This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double-double format, to reduce the effect of the coefficients’ perturbation.
Peibing Du, Hao Jiang 0001, Lizhi Cheng
openaire   +3 more sources

Quantum State‐Resolved Photodissociation Dynamics Study of Transition‐Metal Carbonyl and Nitrosyl

The Chemical Record, EarlyView.
State‐resolved scattering measurements provide experimental visualization of nuclear motions in reacting molecules. Carbonyls and nitrosyls are typical ligands in most of the transition‐metal complexes, which undergo dissociation upon visible and ultraviolet photoexcitation.
Keigo Nagamori, Hiroyuki Nakata, Hiroshi Kohguchi   +2 more
wiley   +1 more source

Orthogonalizing q-Bernoulli polynomials

Demonstratio Mathematica
In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials.
Kuş Semra, Tuglu Naim
doaj   +1 more source

The telephone polynomials: An Appell-type orthogonal polynomials connecting Hermite–Laguerre polynomials

Nuclear Physics B
This article investigates a new Appell-type sequence, the telephone polynomials, which extend the classical telephone (involution) numbers. We present their fundamental algebraic properties, structural characterizations, and diverse interconnections with
Kalika Prasad, Munesh Kumari
doaj   +1 more source

Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation [PDF]

, 2009
A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of ...
Lombardi, Guido
core   +1 more source

Harmonic analysis of little $q$-Legendre polynomials

, 2022
Many classes of orthogonal polynomials satisfy a specific linearization property giving rise to a polynomial hypergroup structure, which offers an elegant and fruitful link to Fourier analysis, harmonic analysis and functional analysis. From the opposite
Kahler, Stefan, Stefan Kahler
core   +1 more source

Diffractive wavefront correction for Fe L‐edge spectroscopy on the meV scale

Journal of Synchrotron Radiation, EarlyView.
We propose an aberration‐corrected, wavelength‐dispersive instrument for soft X‐ray spectroscopy at an energy‐resolving power of (5–6) × 104, designed for, for example, resonant inelastic X‐ray scattering at synchrotron beamlines or X‐ray free‐electron lasers.We propose a wavelength‐dispersive instrument for high‐resolution soft X‐ray spectroscopy at ...
Christoph Braig, Andrey Sokolov, Frank Siewert, Christian Seifert   +3 more
wiley   +1 more source