Search results with tag "Orthogonal polynomials"
Hermite and Laguerre Polynomials
williamsgj.people.cofc.eduHermite and Laguerre Polynomials In this chapter we study two sets of orthogonal polynomials, Hermite and Laguerre polynomials. These sets are less common in mathematical physics than the Legendre and Bessel functions of Chapters 11 and 12, but Hermite polynomials occur in solutions of the simple harmonic oscillator of quantum
Gram-Schmidt Orthogonalization - USM
www.math.usm.eduThat is, any family of orthogonal polynomials satis es a three-term recurrence relation, in which each polynomial depends on the previous two. Table lists several families of orthogonal polynomials that can be generated from such a recurrence relation; we will see some of these families later in the course. Polynomials Scalar Product Legendre R ...
THE RIEMANN HYPOTHESIS - Purdue University
www.math.purdue.educonsecutive orthogonal polynomials have no zeros in a half–plane which is larger than the upper or the lower half–plane. The boundary of the larger half–plane is shifted from the real axis by a distance one–half. The Riemann hypothesis is contained in the issue of explaining the observed shift in