Discrete Hypergeometric Legendre Polynomials [PDF]
Mathematics, 2021 A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials.
Tom Cuchta, Rebecca Luketic
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Predicting Longitudinal Traits Derived from High-Throughput Phenomics in Contrasting Environments Using Genomic Legendre Polynomials and B-Splines. [PDF]
G3 (Bethesda), 2019 Recent advancements in phenomics coupled with increased output from sequencing technologies can create the platform needed to rapidly increase abiotic stress tolerance of crops, which increasingly face productivity challenges due to climate change.
Momen M, Campbell MT, Walia H, Morota G.
europepmc +4 more sources
Congruences concerning Legendre polynomials [PDF]
Proceedings of the American Mathematical Society, 2010 Let $p$ be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for $\sum_{k=0}^{\frac{p-1}2}\binom{2k}k^2m^{-k}\mod {p^2}$. In particular, we confirm several conjectures of Z.W. Sun.
Sun, Zhi-Hong
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The application of Legendre Polynomials to model muscularity and body condition score in primiparous Italian Simmental cattle [PDF]
Italian Journal of Animal Science, 2022 The aim of the present study was to develop a model to predict muscularity and body condition score (BCS) during the lactation of Italian Simmental dairy cows in Emilia Romagna herds.
Giovanni Buonaiuto +6 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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Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel [PDF]
Advances in Continuous and Discrete Models, 2022 In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and
Naveed Ahmad Khan +3 more
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Some results for sums of products of Chebyshev and Legendre polynomials [PDF]
Advances in Difference Equations, 2019 In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials.
Yuan He
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On polar Legendre polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2010 10 pages, no figures.-- MSC2000 codes: Primary 42C05; Secondary 33C25.-- ArXiv pre-print available at: http://arxiv.org/abs/0709.4537Accepted in Rocky Mountain Journal of Mathematics.We introduce a new class of polynomials {Pn}, that we call polar ...
Bello, José Y. +2 more
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O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing [PDF]
, 2012 A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1].
Bogaert, Ignace +2 more
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Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained.
Luc Vinet, Alexei Zhedanov
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