Sökning: "Hermite polynomials"

Visar resultat 1 - 5 av 7 uppsatser innehållade orden Hermite polynomials.

  1. 1. Generating Functions : Powerful Tools for Recurrence Relations. Hermite Polynomials Generating Function

    Kandidat-uppsats, Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

    Författare :Christoffer Rydén; [2023]
    Nyckelord :Ordinary power series generating function; Exponential generating function; Moment generating function; Hermite polynomials;

    Sammanfattning : In this report we will plunge down in the fascinating world of the generating functions. Generating functions showcase the "power of power series", giving more depth to the word "power" in power series. We start off small to get a good understanding of the generating function and what it does. LÄS MER

  3. 2. On orthogonalizing weights for the Hermite polynomials

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Lukas Odelius; [2022]
    Nyckelord :Analysis; orthogonal polynomials; orthogonalizing weights; weights; Hermite; Hermite polynomial; Analys; ortogonala polynom; ortogonaliserande vikter; vikter; Hermite; Hermite polynom;

    Sammanfattning : In this paper we study the orthogonal polynomial system on C (z = x + iy) generated by weights of the form w(x, y) = e^{-Q(x, y)} where Q(x, y) is a positive definite quadratic form, we consider the stability of the polynomial system relative to perturbations to the weights and we construct new orthogonalizing weights for the Hermite polynomials. . LÄS MER

  4. 3. Quantum Mechanical Propagators Related to Classical Orthogonal Polynomials

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Valdemar Melin; [2021]
    Nyckelord :;

    Sammanfattning : A few quantum systems on the line with weighted classical orthogonal polynomials as eigenstates are studied. Explicit expressions of the propagators,i.e. the integral kernels of the time evolution operators, are derived. LÄS MER

  5. 4. A Comparison between Approximations of Option Pricing Models and Risk-Neutral Densities using Hermite Polynomials

    Master-uppsats, Uppsala universitet/Tillämpad matematik och statistik

    Författare :Nathaniel Ahy; [2020]
    Nyckelord :;

    Sammanfattning : .... LÄS MER

  7. 5. Asymptotics of beta-Hermite Ensembles

    Kandidat-uppsats, Linköpings universitet/Matematisk statistik; Linköpings universitet/Tekniska fakulteten

    Författare :Filip Berglund; [2020]
    Nyckelord :beta-Hermite ensembles; Gaussian ensembles; empirical distribution function; level density; largest eigenvalue; order statistic; Sturm sequence; Hermite polynomials; beta-Hermite ensemblerna; gaussiska ensemblerna; empiriska fördelningsfunktionen; nivåtäthet; största egenvärdet; ordningsstatiska; Sturmföljder; Hermitepolynom;

    Sammanfattning : In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). LÄS MER