We extend the results of Goubin, Mauduit and Sárközy on the well-distribution measure and the correlation measure of order k of the sequence of Legendre sequences with polynomial argument in several ways. We analyze sequences of quadratic characters of finite fields of prime power order and consider in each case two, in general, different definitions of well-distribution measure and correlation...

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-inde...

Motivated by recent works of Sun and Tauraso, we prove some variations on the Green-Krammer identity involving central q-binomial coefficients, such as n−1 ∑ k=0 (−1)kq−(k+1 2 ) [ 2k k ] q ≡ (n 5 ) q−bn 4/5c (mod Φn(q)), where ( n p ) is the Legendre symbol and Φn(q) is the nth cyclotomic polynomial. As consequences, we deduce that 3am−1 ∑

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

We study the application of formal diffeomorphisms to scalar fields. give a new proof that interacting tree amplitudes vanish in resulting theories. Our is directly at diagrammatic level, not appealing path integral, and proceeds via generating function analysis, so it more insightful than previous proofs. Along way, we combinatorial proofs some Bell polynomial identities, comment on connection...

This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical foundation of the spectral approximation is first introduced, based on the Gauss quadratures. The two usual basis of Legendre and Chebyshev polynomials are then p...

The possible role of Rédei polynomials over fields of characteristic zero in the quest for solutions to problems in the study of geometries and vector spaces over finite fields is discussed. This note is exploratory and does not attempt to solve any particular problem, although an example problem is considered.

—An explicit formula for the Fourier coef cients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to an...

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...