Orthogonal polynomials | Special hypergeometric functions

Jacobi polynomials

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight on the interval . The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The Jacobi polynomials were introduced by Carl Gustav Jacob Jacobi. (Wikipedia).

Jacobi polynomials
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Jacobian matrix example

Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT

From playlist Several Variable Calculus / Vector Calculus

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Intro to the Jacobian

Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT

From playlist Several Variable Calculus / Vector Calculus

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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

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Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function

In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL

From playlist Etale Theta

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The Jacobian matrix

An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.

From playlist Multivariable calculus

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Jacobian and Chain Rule

Example discussing the Chain Rule for the Jacobian matrix. Free ebook http://tinyurl.com/EngMathYT

From playlist Several Variable Calculus / Vector Calculus

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Introduction to number theory lecture 35 Jacobi 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 define the Jacobi symbol and prove its basic properties, and show how to calculate it fa

From playlist Introduction to number theory (Berkeley Math 115)

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Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations

Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3

From playlist Solving Systems of Nonlinear Equations

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Newton's Method for Systems of Nonlinear Equations

Generalized Newton's method for systems of nonlinear equations. Lesson goes over numerically solving multivariable nonlinear equations step-by-step with visual examples and explanation of the Jacobian, the backslash operator, and the inverse Jacobian. Example code in MATLAB / GNU Octave on

From playlist Newton's Method

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Advice Maths Research | The Jacobi polynumber maxel challenge! | Wild Egg Maths

We introduce the Jacobi polynomials which are extensions, in some sense, of the Gegenbauer polynomials and play a major role in representation theory. In this talk we outline explorations that you can make, following the two-dimensional maxel approach to number theory and orthogonal polyno

From playlist Maxel inverses and orthogonal polynomials (non-Members)

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A Family of Rationally Extended Real and PT Symmetric Complex Potentials by Rajesh Kumar Yadav

PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a

From playlist Non-Hermitian Physics (ONLINE)

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Sarah Post: Rational extensions of superintegrable systems, exceptional polynomials & Painleve eq.s

Abstract: In this talk, I will discuss recent work with Ian Marquette and Lisa Ritter on superintegable extensions of a Smorodinsky Winternitz potential associated with exception orthogonal polynomials (EOPs). EOPs are families of orthogonal polynomials that generalize the classical ones b

From playlist Integrable Systems 9th Workshop

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A class of exactly solvable extended potentials associated by Rajesh Kumar Yadav

Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys

From playlist Non-Hermitian Physics - PHHQP XVIII

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Martin Gander: On the invention of iterative methods for linear systems

HYBRID EVENT Recorded during the meeting "1Numerical Methods and Scientific Computing" the November 9, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on

From playlist Numerical Analysis and Scientific Computing

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Maria Charina: Algebraic multigrid and subdivision

Abstract: Multigrid is an iterative method for solving large linear systems of equations whose Toeplitz system matrix is positive definite. One of the crucial steps of any Multigrid method is based on multivariate subdivision. We derive sufficient conditions for convergence and optimality

From playlist Numerical Analysis and Scientific Computing

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Central Limit Theorems for linear statistics for biorthogonal ensembles - Maurice Duits

Maurice Duits SU April 2, 2014 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Jim Bryan : Curve counting on abelian surfaces and threefolds

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry

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Tim Scrimshaw - Canonical Grothendieck polynomials with free fermions

A now classical method to construct the Schur functions is constructing matrix el- ements using half vertex operators associated to the classical boson-fermion cor- respondence. This construction is known as using free fermions. Schur functions are also known to be polynomial representativ

From playlist Combinatorics and Arithmetic for Physics: Special Days 2022

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Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.

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Intro to Jacobian + differentiability

A lecture that introduces the Jacobian matrix and its determinant. Such ideas may be thought of as a general derivative of a vector-valued function of many variables and find uses in integration theory.

From playlist Several Variable Calculus / Vector Calculus

Related pages

Continuous q-Jacobi polynomials | Carl Gustav Jacob Jacobi | Classical orthogonal polynomials | Pseudo Jacobi polynomials | Askey–Gasper inequality | Little q-Jacobi polynomials | Rodrigues' formula | Mehler–Heine formula | Romanovski polynomials | Gegenbauer polynomials | Hypergeometric function | Chebyshev polynomials | Big q-Jacobi polynomials | Wigner D-matrix | Gamma function | Mathematics | Principal branch | Legendre polynomials | Zernike polynomials | Orthogonal polynomials | Domain (mathematical analysis) | Generating function