Results 51 to 60 of about 49,043 (210)
A Legendre Polynomial Integral [PDF]
Mathematics of Computation, 1979 Let { P n ( x ) } \{ {P_n}(x)\} be the usual Legendre polynomials. The following integral is apparently new. \[ ∫ 0 1 P n ( 2 x
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This review aims to provide a broad understanding for interdisciplinary researchers in engineering and clinical applications. It addresses the development and control of magnetic actuation systems (MASs) in clinical surgeries and their revolutionary effects in multiple clinical applications.
Yingxin Huo +3 more
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Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative
Mathematical and Computational ApplicationsIn this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation.
Francisco Martínez +2 more
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On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials
Mathematics, 2020 The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are ...
Mohra Zayed +3 more
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ChemPhysChem, Volume 26, Issue 6, March 15, 2025.The solvation structure and dynamics of the SCN− anion in mixed N, N‐Dimethylformamide (DMF)‐water liquid solvents is investigated using classical molecular dynamics simulations. A preferential solvation of SCN− by the water molecules is observed in the first hydration shell, followed by a second shell consisting by both DMF and water molecules.
Ioannis Skarmoutsos, Ilias G. Karvounis
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International Journal of Mathematics and Mathematical Sciences, 1985 The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series
Paul W. Haggard
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Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets [PDF]
, 2015 A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support.
Carvalho Jr, M. A. +3 more
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Study on fracture parameter calibration and failure characteristics of rock with hole and crack
Deep Underground Science and Engineering, EarlyView.The SIF and plastic zone equations for a single hole and crack have been derived. The model's failure state leads to the identification of four types of cracks. The plastic zone increases with increased brittleness and decreased crack length. Abstract Cracks within the surrounding rock of roadways significantly affect their stability and failure ...
Shaochi Peng, Wensong Wang
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This study examines the combined impact of different thermal conductivity and viscosity on unsteady non‐Newtonian Casson fluid flow of incompressible, electrical conductivity in a porous vertical channel with convective cooling walls, uniform magnetic field, and constant pressure gradient.
A. S. Adeyemo +2 more
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A Property of Legendre Polynomials [PDF]
Proceedings of the National Academy of Sciences, 1970 Remark I: The Legendre polynomials are the spherical functions for the symmetric space SO(3)/SO(2). A property analogous to that stated in the above theorem holds for other symmetric spaces. In this fashion we get also new properties for Gegenbauer polynomials, Bessel, and Legendre functions.
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