LEGENDRE_SHIFTED_POLYNOMIAL is a C++ library which evaluates the shifted Legendre polynomial. The standard Legendre polynomial P(n,x) is defined over the interval [-1,+1]. The shifted Legendre ...

The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of ...

The script performs projections of a function onto a set of orthogonal polynomials, specifically Legendre polynomials, over a given interval. These polynomials are generated and normalized using the ...

Complementary polynomials of Legendre polynomials are briefly presented, as well as those for the confluent and hypergeometric functions, relativistic Hermite polynomials and corresponding new ...

Abstract This paper presents the connections between univariate and bivariate Hermite polynomials and associated differential equations with specific representations of 𝔰𝔩(2,𝑅) algebra whose Cartan ...

Abstract: We model non stationary signals by assuming that the phase and the amplitude are both a polynomial function of time on a short finite interval. The used functions are normalized Legendre ...

The present paper introduces a method of basis transformation of a vector space that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such ...

This is a preview. Log in through your library . Abstract The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state ...

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...

ABSTRACT: Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of ...