Elliptic functions | Theta functions
There are a number of notational systems for the Jacobi theta functions. The notations given in the Wikipedia article define the original function which is equivalent to where and . However, a similar notation is defined somewhat differently in Whittaker and Watson, p. 487: This notation is attributed to "Hermite, H.J.S. Smith and some other mathematicians". They also define This is a factor of i off from the definition of as defined in the Wikipedia article. These definitions can be made at least proportional by x = za, but other definitions cannot. Whittaker and Watson, Abramowitz and Stegun, and Gradshteyn and Ryzhik all follow Tannery and Molk, in which Note that there is no factor of π in the argument as in the previous definitions. Whittaker and Watson refer to still other definitions of . The warning in Abramowitz and Stegun, "There is a bewildering variety of notations...in consulting books caution should be exercised," may be viewed as an understatement. In any expression, an occurrence of should not be assumed to have any particular definition. It is incumbent upon the author to state what definition of is intended. (Wikipedia).
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
Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
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
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
This video explains how to calculator a Jacobian for a change of variables.
From playlist Applications of Double Integrals: Mass, Center of Mass, Jacobian
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.
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Find the Jacobian Given x=au+bv, y=u^2+cv
This video explains how to determine the Jacobian given the equations of a transformation. http://mathispower4u.com
From playlist Applications of Double Integrals: Mass, Center of Mass, Jacobian
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
60 Sritharan - Stochastic Navier-Stokes equations - solvability & control
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Arnold diffusion and Mather theory - Ke Zhang
Emerging Topics Working Group Topic: Arnold diffusion and Mather theory Speaker: Ke Zhang Affiliation: University of Toronto Date: April 11, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Optimal Transportation and Applications - 12 November 2018
http://crm.sns.it/event/436 It is the ninth edition of this "traditional'' meeting in Pisa, after the ones in 2001, 2003, 2006, 2008, 2010, 2012, 2014 and 2016. Organizing Committee Luigi Ambrosio, Scuola Normale Superiore, Pisa Giuseppe Buttazzo, Dipartimento di Matematica, Università
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Stephen GUSTAFSON - Stability of periodic waves of 1D nonlinear Schrödinger equations
Motivated by the more general problem of classifying NLS dynamics in the presence of a potential, we consider the case of a (suitably) small, repulsive potential, and for certain nonlinearities, classify solutions near the 'pinned' ground state according to classical trajectories. Joint wo
From playlist Trimestre "Ondes Non linéaires" - Summer school
Weak Stability Boundary and Capture in the Three-Body Problem - Edward Belbruno
Edward Belbruno NASA/AISR & IOD, Inc. January 19, 2011 GEOMETRY/DYNAMICAL SYSTEMS The problem of capture in the planar restricted three-body problem is addressed. In particular, weak capture is described, which occurs at a complicated region called the weak stability boundary, where the m
From playlist Mathematics
Arnold Diffusion by Variational Methods III - John Mather
John Mather Princeton University; Institute for Advanced Study November 9, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
inverse functions
From playlist PIXL PPE Paper 2 June 2016 Higher Tier AQA Style Worked Solutions
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 5
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
Sepideh Mirrahimi : Integro-differential models of evolutionary adaptation in changing...- lecture 2
What would be the impact of an environment change on the persistence and the genetic/phenotypic distribution of a population? We present some integro-differential models describing the evolutionary adaptation of asexual phenotypically structured populations subject to mutation and selectio
From playlist CEMRACS 2022
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 3
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1