Results 11 to 20 of about 1,847 (220)
Insight into Genome-Wide Associations of Growth Trajectories Using a Hierarchical Non-Linear Mixed Model [PDF]
BiologyIn applying a hierarchical mixed model to genome-wide association analysis (GWAS) of longitudinal data, dimensionality reduction through modeling repeated measurements improves both computational efficiency and statistical power. Legendre polynomials can
Ying Zhang +3 more
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Some applications of Legendre numbers [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers.
Paul W. Haggard
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On an Inequality for Legendre Polynomials [PDF]
Mathematics, 2020 This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper.
Florin Sofonea, Ioan Ţincu
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The overlap integral of three associated Legendre polynomials [PDF]
Applied Mathematics Letters, 2002 The author derives a formula for the so-called overlap integral of three associated Legendre functions (mistakenly called ``polynomials'') in form of a double sum. The result is generalized to the case of \(n\) Legendre functions \((n\geq 3\), integer). For the proof well-known formulas for the integral with one and two Legendre functions and a formula
Shi-Hai Dong, Renato Lemus
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Sums of finite products of Legendre and Laguerre polynomials [PDF]
Advances in Difference Equations, 2018 In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them.
Taekyun Kim +3 more
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Radii problems for some classes of analytic functions associated with Legendre polynomials of odd degree [PDF]
Journal of Inequalities and Applications, 2020 The aim of the present paper is to study radii problems for two general classes including various known subclasses of analytic functions associated with the normalized form of Legendre polynomials of odd degree.
Ali Ebadian +4 more
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Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials [PDF]
Mathematics, 2021 In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are ...
Abdel Moneim Y. Lashin +2 more
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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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A generalized formula for the integral of three associated Legendre polynomials [PDF]
Applied Mathematics Letters, 1999 The authors present here a recurrence method for determining integrals \[ \int_{-1}^1 \prod_{k=1}^N P_{j_k}^{m_k} (z) dz,\qquad N=1,2,\dots, \] where the \[ P_j^m(z)= {1\over{\Gamma(1-m)}} \left( {z+1}\over{z-1}\right)^{m/2} \;_2F_1\Biggl[-j,j+1; 1-m; {{1-z}\over{2}} \Biggr] \] are associated Legendre polynomials. The application of the authors' method,
Mavromatis, H.A., Alassar, R.S.
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Regional Geomagnetic Field Modeling Based on Associated Legendre Polynomials
Applied SciencesGlobal geomagnetic field models typically have low spatial resolution, whereas regional models are constrained by boundary effects and limited truncation levels.
Libo Zhu +4 more
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