Orthogonal polynomials | Q-analogs | Special hypergeometric functions

Discrete q-Hermite polynomials

In mathematics, the discrete q-Hermite polynomials are two closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Carlitz. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw give a detailed list of their properties. hn(x;q) is also called discrete q-Hermite I polynomials and ĥn(x;q) is also called discrete q-Hermite II polynomials. (Wikipedia).

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Hermite differential equation

Series solution of the Hermite differential equation. Shows how to construct the Hermite polynomials. Join me on Coursera: Differential equations for engineers https://www.coursera.org/learn/differential-equations-engineers Matrix algebra for engineers https://www.coursera.org/learn/matr

From playlist Differential Equations with YouTube Examples

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Ch02n3: Hermite interpolation

Hermite interpolation. Numerical methods, chapter 2, additional video no 3. To be viewed after video Ch02n2. Wen Shen, Penn State University, 2018.

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices - Shcherbina

Tatyana Shcherbina Institute for Low Temperature Physics, Kharkov November 1, 2011 We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices Hn=n−1/2WnHn=n−1/2Wn and the hermitian sample covariance matrices Xn=n−1A∗m,nAm,nXn=n−1Am,n

From playlist Mathematics

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Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (56 of 92) What is a Hermite Polynomial?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Hermite polynomial. Previous videos showed the solution best describe the quantum oscillator of the Schrodinger equation is the product of a constant that needed to be normalized, mu

From playlist THE "WHAT IS" PLAYLIST

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Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (57 of 92) Calculating Hermite Polynomial?

Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the first few Hermitian polynomials stating with n=0 to n=3. Next video in this series can be seen at: https://youtu.be/9euxAKJDll0

From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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Phong NGUYEN - Recent progress on lattices's computations 2

This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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Frédéric Chyzak

Generalized Hermite Reduction, Creative Telescoping, and Definite Integration of D-Finite Functions Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of a

From playlist DART X

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Math 060 Fall 2017 112717C Hermitian Matrices Part 1

Definitions: complex conjugate, modulus, complex vector, conjugate transpose, complex inner product, conjugate matrix. Hermitian matrices. Hermitian matrices and the inner product. Hermitian matrices have 1. real eigenvalues, 2. orthogonal eigenspaces. Unitary matrices. Hermitian matr

From playlist Course 4: Linear Algebra (Fall 2017)

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Li Wang: An asymptotic preserving method for Levy Fokker Planck equation with fractional...

CIRM VIRTUAL EVENT Recorded during the meeting "Kinetic Equations: from Modeling, Computation to Analysis" the March 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide m

From playlist Virtual Conference

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Giovanni Peccati: Some applications of variational techniques in stochastic geometry I

Some variance estimates on the Poisson space, Part I I will introduce some basic tools of stochastic analysis on the Poisson space, and describe how they can be used to develop variational inequalities for assessing the magnitude of variances of geometric quantities. Particular attention

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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A central limit theorem for Gaussian polynomials... pt1 -Anindya De

Anindya De Institute for Advanced Study; Member, School of Mathematics May 13, 2014 A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions In this talk, we will continue, the proof of the Central Limit theorem from my las

From playlist Mathematics

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Differential Equations | Second order linear homogeneous equations with repeated roots.

We derive the general solution to a second order linear homogeneous differential equation with constant coefficients whose companion polynomial has a repeated root.

From playlist Linear Differential Equations

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Eigenvalue bounds on sums of random matrices - Adam Marcus

Members’ Seminar Topic:Eigenvalue bounds on sums of random matrices Speaker: Adam Marcus Affilation: Princeton University Date: November 14, 2016 For more videos, visit http://video.ias.edu

From playlist Mathematics

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(7.2.1C) Power Series Solution to Hermite's Equation: y''-2xy'+2ny=0

This video explains how to determine a power series solution to a second order linear ordinary differential equation. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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"Transcendental Number Theory: Recent Results and Open Problem​s" by Prof. Michel Waldschmidt​

This lecture will be devoted to a survey of transcendental number theory, including some history, the state of the art and some of the main conjectures.

From playlist Number Theory Research Unit at CAMS - AUB

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The Characteristic Polynomial

The definition of the characteristic polynomial (without using determinants). The Cayley-Hamilton Theorem.

From playlist Linear Algebra Done Right

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Phong NGUYEN - Recent progress on lattices's computations 1

This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

Related pages

Orthogonal polynomials | Al-Salam–Carlitz polynomials | Askey scheme