Mathematical identities | Theta functions | Theorems in number theory | Elliptic functions | Infinite products
In mathematics, the Jacobi triple product is the mathematical identity: for complex numbers x and y, with |x| < 1 and y ≠ 0. It was introduced by Jacobi in his work Fundamenta Nova Theoriae Functionum Ellipticarum. The Jacobi triple product identity is the Macdonald identity for the affine root system of type A1, and is the Weyl denominator formula for the corresponding affine Kac–Moody algebra. (Wikipedia).
Triple Integrals: Change of Three Variables Using the Jacobian
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From playlist Triple Integrals in Cylindrical and Spherical Coordinates / Change of Variables (Jacobian)
What is the scalar triple product of vectors and how do we compute it? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/KiMe1ZadrV
From playlist Introduction to Vectors
Rogers-Ramanujan Identities | Part 7: The Jacobi Triple Product
We develop another tool which will be used to prove the Rogers-Ramanujan Identites. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Rogers-Ramanujan Identities
Example of a Change of Variables for a Double Integral: Jacobian
http://mathispower4u.yolasite.com/
From playlist Triple Integrals in Cylindrical and Spherical Coordinates / Change of Variables (Jacobian)
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
This video explains how to determine the volume of a parallelepiped using the triple scalar product. http://mathispower4u.yolasite.com/
From playlist Vectors
Region between x^2+y^2 and 2x+y+1
From playlist Triple integrals
Scalar triple product and volume
How to calculate the volume of parallelpipeds via scalar triple product of vectors. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link)
From playlist Introduction to Vectors
By popular demand, I'm showing how to change variables in multivariable calculus using the Jacobian, and in particular I want to show that it is not much different from the u-substitution technique in single variable calculus. Enjoy! Note: I messed up the bounds in the end of the video; t
From playlist Double and Triple Integrals
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
Ramanujan's Theta Functions -- Number Theory 32
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From playlist Number Theory
Ramanujan's Theta Functions -- Number Theory 32
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From playlist Number Theory v2
Mohamed Boucetta: On the geometry of noncommutative deformations
Recording during the meeting "Workshop on Differential Geometry and Nonassociative Algebras" the November 12, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Geometry
Ramanujan's famous (mod 5) congruence -- Number Theory 33
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From playlist Number Theory v2
Ramanujan's famous mod 5 congruence — Number Theory 33
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.
From playlist Number Theory
Brent Pym: Holomorphic Poisson structures - lecture 1
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the April 28, 2020 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 Virtual Conference
Colloquium MathAlp 2019 - Richard Montgomery
Oscillating about coplanarity in the 4 body problem For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known res
From playlist Colloquiums MathAlp
Extensions of the Gross-Zagier formula - Kartik Prasanna
Kartik Prasanna University of Michigan April 23, 2015 I will first discuss the general conjectural picture relating algebraic cycles to L-functions and some extensions of the Gross-Zagier formula involving pp-adic L-functions. This leads naturally to the question of constructing algebraic
From playlist Mathematics
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