Results 81 to 90 of about 136,517 (223)
Legendre polynomial order selection in projection pursuit density estimation
Lietuvos Matematikos Rinkinys, 2013 Projection pursuit method and its application to probability density estimation is discussed. Method proposed by J.H. Friedman, based on projection density estimation using orthogonal Legendre polynomials, is analysed.
Mindaugas Kavaliauskas
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Congruences concerning Legendre polynomials II [PDF]
Journal of Number Theory, 2013 Suppose that p is an odd prime and d is a positive integer. Let x and y be integers given by p = x2+dy2 or 4p = x2+dy2. In this paper we determine x( mod p) for many values of d. For example, [Formula: see text] where x is chosen so that x ≡ 1 ( mod 3). We also pose some conjectures on supercongruences modulo p2 concerning binary quadratic forms.
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Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
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Magnetic Resonance in Medicine, Volume 96, Issue 5, Page 2489-2504, November 2026.ABSTRACT Purpose To improve the accuracy of diffusion‐weighted powder average signals for diffusion encoding with arbitrary b‐tensors. Methods We identify an intrinsic dihedral (D2) symmetry of diffusion signals for arbitrary diffusion encoding, which defines their natural signal space (a quotient of 3D rotations). Based on this, we propose a method to
Sune Nørhøj Jespersen +1 more
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On the Expansion of Legendre Polynomials in Bicomplex Space and Coupling with Fractional Operators
AxiomsIn this paper, we introduce a novel version of the Legendre polynomials in the bicomplex system. We investigate the essential properties of the Legendre polynomial, focusing on its bicomplex structure, generating functions, orthogonality, and recurrence ...
Ahmed Bakhet +3 more
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Notes on Legendre polynomials [PDF]
Bulletin of the American Mathematical Society, 1945 Not ...
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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].
Fostier, Jan +2 more
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Analysis of Eigenvalue Clustering Leads to Optimal Scaling in Numerical Radiative Transfer
Numerical Linear Algebra with Applications, Volume 33, Issue 5, October 2026.ABSTRACT We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, that is, anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates (SN$$ {S}_N $$) discretization, we report the corresponding matrix structures, depending on the model and
Pietro Benedusi +3 more
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Definite Integrals using Orthogonality and Integral Transforms
Symmetry, Integrability and Geometry: Methods and Applications, 2012 We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Howard S. Cohl, Hans Volkmer
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Comparison of Random Regression Models with Different Order Legendre Polynomials for Genetic Parameter Estimation on Race Completion Speed of Arabian Horses. [PDF]
Animals (Basel), 2022 Önder H +6 more
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