An introduction to Legendre Polynomials and the Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
An example of expanding a function in a Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
Legendre Symbol Definition and Example
Intro to quadratic residues: https://youtu.be/M6gDsFhQugM The Legendre symbol is a useful notation for describing whether a number is a quadratic residue mod p. Here we explain what the Legendre symbol is and do a practice example with quadratic residues mod 5. Quadratic Residues playli
From playlist Quadratic Residues
Introduction to number theory lecture 32. Calculation of the Legendre symbol
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We use Gauss's lemma to find out when -2, 3, 5, are quadratic residues of a prime and give
From playlist Introduction to number theory (Berkeley Math 115)
Legendre's Formula and prove that the product of n consecutive integers is divisible by n factorial
We prove a common fact in number theory: the product of n consecutive integers is divisible by n factorial Reference: 1. p-adic valuation https://en.wikipedia.org/wiki/P-adic_valuation 2. Legendre Formula for p-adic valuation for n factorial: https://en.wikipedia.org/wiki/Legendre%27s_f
From playlist Elementary Number Theory
[Lesson 25] QED Prerequisites Scattering 2
We follow the derivation of the associated Legendre polynomials using the reference "The Functions of Mathematical Physics" by Harry Hochstadt as our guide. The goal is to take ownership of these functions so we can confidently advance our understanding of the partial wave expansion of pla
From playlist QED- Prerequisite Topics
Introduction to Spherical Harmonics
Using separation of variables in spherical coordinates, we arrive at spherical harmonics.
From playlist Quantum Mechanics Uploads
How To Use Legendre Polynomials In Python
Legendre Polynomial pop up quite a few times in your physics degree. In this video I show you how to write a python code to plot out any degree legendre polynomial!
From playlist Daily Uploads
Advice for Research Maths | Properties of Legendre and Gegenbauer polynomials | Wild Egg Maths
To try to understand how to apply two dimensional maxel magic to the family of Legendre polynomials, let's look at some properties of these polynumbers, including differential equations, connections with Chebyshev polynomials, and how they arise from the geometry of the sphere and an assoc
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Completeness and Orthogonality
A discussion of the properties of Completeness and Orthogonality of special functions, such as Legendre Polynomials and Bessel functions.
From playlist Mathematical Physics II Uploads
Separation of Variables - Spherical Coordinates (Part 1)
We setup the problem of separation of variables for spherical coordinates by studying the steady-state temperature of a spherical ball with some temperature specified on its boundary. The solution involves Legendre Polynomials.
From playlist Mathematical Physics II Uploads
[Lesson 26] QED Prerequisites Scattering 3: The radial wave function of a free particle
In this lesson we explore the spherical Bessel, Neuman, and Hankel functions which are all critical to our understanding of scattering theory. We will just accept the standard solutions, and explore the properties of the functions, except for the most important property: their asymptotic f
From playlist QED- Prerequisite Topics
Number Theory | The Legendre Symbol and Euler's Criterion
We present a definition of the Legendre symbol and Euler's criterion to calculate it quickly. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
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
Gaussian Quadrature | Lecture 40 | Numerical Methods for Engineers
An explanation of Gaussian quadrature. An example of how to calculate the weights and nodes for two-point Legendre-Gauss quadrature. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engi
From playlist Numerical Methods for Engineers