In mathematics, the q-expansion principle states that a modular form f has coefficients in a module M if its q-expansion at enough cusps resembles the q-expansion of a modular form g with coefficients in M. It was introduced by Katz . (Wikipedia).
Principle of Mathematical Induction (ab)^n = a^n*b^n Proof
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From playlist Proofs
Binomial expansion to the sixth power
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
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Using binomial expansion to expand a binomial to the fourth degree
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
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Expand a binomial to the fifth power
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
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Find the third term of a binomial to the sixth power
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
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On the GrossβStark conjecture 2 by Mahesh Kakde
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
Second Order Recurrence Formula (1 of 3: Prologue - considering the old course)
More resources available at www.misterwootube.com
From playlist Further Proof by Mathematical Induction
Thermodynamics 4a - Entropy and the Second Law I
The Second Law of Thermodynamics is one of the most important laws in all of physics. But it is also one of the more difficult to understand. Central to it are the concepts of reversibility and entropy. Note on the definition of a "closed system." I am using the term "closed system" in th
From playlist Thermodynamics
The Analytic S-matrix Bootstrap (Lecture - 02) by Alexander Zhiboedov
STRING THEORY LECTURES THE ANALYTIC S-MATRIX BOOTSTRAP SPEAKER: Alexander Zhiboedov (Theory Division, CERN, Geneva) DATE: 29 January 2019 to 31 January 2019 VENUE: Emmy Noether Seminar Room, ICTS Bangalore Lecture 1: Jan 29, 2019 at 11:00 am Lecture 2: Jan 30, 2019 at 11:00 am Lecture
From playlist Infosys-ICTS String Theory Lectures
The Large SpeNta Limit by David Gross
11 January 2017 to 13 January 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but
From playlist String Theory: Past and Present
Studying thermal QCD matter on the lattice (LQCD1 - Lecture 1) by Peter Petreczky
PROGRAM THE MYRIAD COLORFUL WAYS OF UNDERSTANDING EXTREME QCD MATTER ORGANIZERS: Ayan Mukhopadhyay, Sayantan Sharma and Ravindran V DATE: 01 April 2019 to 17 April 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Strongly interacting phases of QCD matter at extreme temperature and
From playlist The Myriad Colorful Ways of Understanding Extreme QCD Matter 2019
How to use binomial expansion to expand a binomial to the 7th power
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
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Amplitudes Meet LIGO by Chia-Hsien Shen
PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onlin
From playlist Recent Developments in S-matrix Theory (Online)
Faouzi Triki: Inverse scattering problems with multi-frequency data
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 Partial Differential Equations
How can we represent any term in a binomial expansion
π Learn all about binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula for a binomial expans
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The Generalized Ramanujan Conjectures and Applications (Lecture 2) by Peter Sarnak
Lecture 2: Thin Groups and Expansion Abstract: Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski dense in SL(n), arise in many geometric and diophantine problems (eg as reflection groups,groups connected with elementary geometry such as integral apollonian packings,
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
12. Perturbative Renormalization Group Part 4
MIT 8.334 Statistical Mechanics II: Statistical Physics of Fields, Spring 2014 View the complete course: http://ocw.mit.edu/8-334S14 Instructor: Mehran Kardar In this lecture, Prof. Kardar continues his discussion on the Perturbative Renormalization Group, including the Irrelevance of Oth
From playlist MIT 8.334 Statistical Mechanics II, Spring 2014
Using binomial expansion to expand a binomial to the fourth power
π Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power. The general formula
From playlist Sequences