The Inverse Polynomial Reconstruction Method (IPRM) has been recently introduced by J.-H. Jung and B. Shizgal in order to remedy the Gibbs phenomenon, see [2], [3], [4], [5]. Their main idea is to reconstruct a given function from its n Fourier coefficients as an algebraic polynomial of degree n− 1. This leads to an n × n system of linear equations, which is solved to find the Legendre coeffici...

The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [J. Opt. Soc. Am. B24, 2676 (2007)], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagn...

Abstract We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row and the column indices vanishes iff n is composite. If the dimension is a prime p, then the determinant evaluates to a polynomial of degree p−1 which is the product of a power of p and the generating polynomial of the partial sums of Legendr...

Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant fBc , and revisit fB and fBs . Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are fBc = 528 ± 19 MeV, fB = 186 ± 14 MeV, and fBs = 222± 12 M...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

The aim of this research is an improvement of plant seedling recognition by two new approaches of shape feature generation based on plant silhouettes. Experiments show that the proposed feature sets possess value in plant recognition when compared with other feature sets. Both methods approximate a distance distribution of an object, either by resampling or by approximation of the distribution ...

random regression models (rrm) have become common for the analysis of longitudinal data or repeated records on individual over time. the goal of this paper was to explore the use of random regression models with orthogonal / legendre polynomials (rrl) to analyze new repeated measures called clutch size (cs) as a meristic trait for iranian native fowl. legendre polynomial functions of increasing...

We continue to investigate binary sequence (fu) over {0, 1} defined by (−1)fu = ( (u−u)/p p ) for integers u ≥ 0, where ( · p ) is the Legendre symbol and we restrict ( 0 p ) = 1. In an earlier work, the linear complexity of (fu) was determined for w = p − 1 under the assumption of 2p−1 6≡ 1 (mod p2). In this work, we give possible values on the linear complexity of (fu) for all 1 ≤ w < p− 1 un...