Chebyshev polynomials are a sequence of orthogonal polynomials that arise in various areas of mathematics, particularly in approximation theory, numerical analysis, and polynomial interpolation.

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).

Abstract: This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they ...

Abstract: We present here an algorithm for factoring a given polynomial over GF(q) into powers of irreducible polynomials. The method reduces the factorization of a polynomial of degree m over GF(q) ...

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such ...

Orthogonal polynomials play a significant role in quantum mechanics, particularly in solving differential equations that describe physical systems. These polynomials are used to construct ...

Chebyshev polynomials are a special class of polynomials that have some remarkable properties. They are defined by the recurrence relation Tn(x) = 2xTn-1(x) - Tn-2(x), with T0(x) = 1 and T1(x ...

We assume a one-dimensional robot motion x(t) at time t is formulated as a quintic polynomials based on time as follows: x(t) = a_0+a_1t+a_2t^2+a_3t^3+a_4t^4+a_5t^5 a ...

State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, People’s Republic of China School of Chemical Sciences, University ...

B-splines are poor in performance and not very intuitive to use. I'm trying to replace B-splines with Jacobi polynomials. Jacobi polynomials are orthogonal polynomials defined on the interval [-1, 1].