Meromorphic functions | Gamma and related functions | Special hypergeometric functions
In mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles. The gamma function has no zeroes, so the reciprocal gamma function 1/Γ(z) is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: Other extensions of the factorial function do exist, but the gamma function is the most popular and useful. It is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics. (Wikipedia).
Number Theory 1.2 : The Gamma Function
In this video, I introduce the gamma function and show a few properties of it. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
The Gamma Function for Half Integer Values
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From playlist Number Theory
From playlist Probability Distributions
The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!
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From playlist Limits
Complex analysis: Gamma function
This lecture is part of an online undergraduate course on complex analysis. We describe the basic properties of the gamma function, including its functional equations and the duplication formula, and give a characterization of it in terms of its functional equation and growth rate. Corr
From playlist Complex analysis
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Beta Function - Integral Representation Derivation
Today, we derive the integral representation for the Beta function. We will be using this result in a future video to prove the Euler reflection formula!
From playlist Integrals
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.
From playlist Determining Inverse Functions
In this video, we begin looking at inverse functions. We do not worry about the domain and range of the inverse function, we focus only on finding the rule for the inverse function. The domain and range of the inverse function will be covered in future videos. We do, however, include an ex
From playlist All Videos
Vincent Vargas - 4/4 Liouville conformal field theory and the DOZZ formula
Materials: http://marsweb.ihes.fr/Cours_Vargas.pdf Liouville conformal field theory (LCFT hereafter), introduced by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strings", can be seen as a random version of the theory of Riemann surfaces. LCFT appears in Polyakov's work a
From playlist Vincent Vargas - Liouville conformal field theory and the DOZZ formula
What is a Manifold? Lesson 10: Tangent Space - Basis Vectors
What is a Manifold? Lesson 10: Tangent Space - Basis Vectors
From playlist What is a Manifold?
Euler-Mascheroni X: The Trial of Jens
Channel social media: Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Twitter: @whatthehectogon https://twitter.com/whatthehectogon Any questions? Leave a comment below or email me at the misspelled whatthehectagon@gmail.com In this video, I finally present the a
From playlist The Generalization War
The Beta Function and Legendre's Duplication Formula
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From playlist Analysis
The Pi Function - An Overview of Identities
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From playlist Number Theory
The dynamical Φ43Φ34 model: derivation of the renormalised equations - Martin Hairer
Martin Hairer University of Warwick March 5, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
ODE existence and uniqueness theorem
In this video, I prove the famous Picard-Lindelöf theorem, which states that, if f is Lipschitz, then the ODE y’ = f(y) with a given initial condition always has a unique solution (at least in the local sense). The proof involves some neat analysis; more precisely we use the Banach fixed p
From playlist Real Analysis
Gaussian Integral 6 Gamma Function
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using properties of the gamma function, which
From playlist Gaussian Integral
Euler-Mascheroni XII: A Couple Moments of Reflection
Channel social media: Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Twitter: @whatthehectogon https://twitter.com/whatthehectogon Any questions? Leave a comment below or email me at the misspelled whatthehectagon@gmail.com Here I present a proof for the reflect
From playlist Analysis