In mathematics, the multivariate gamma function ฮp is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the probability density function of the Wishart and inverse Wishart distributions, and the matrix variate beta distribution. It has two equivalent definitions. One is given as the following integral over the positive-definite real matrices: where denotes the determinant of . The other one, more useful to obtain a numerical result is: In both definitions, is a complex number whose real part satisfies . Note that reduces to the ordinary gamma function. The second of the above definitions allows to directly obtain the recursive relationships for : Thus * * and so on. This can also be extended to non-integer values of with the expression: Where G is the Barnes G-function, the indefinite product of the Gamma function. The function is derived by Anderson from first principles who also cites earlier work by Wishart, Mahalanobis and others. There also exists a version of the multivariate gamma function which instead of a single complex number takes a -dimensional vector of complex numbers as its argument. It generalizes the above defined multivariate gamma function insofar as the latter is obtained by a particular choice of multivariate argument of the former. (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
What are the Inverse Trigonometric functions and what do they mean?
๐ Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-
From playlist Evaluate Inverse Trigonometric Functions
(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
Evaluate inverse of cosecant using a calculator
๐ Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-
From playlist Evaluate Inverse Trigonometric Functions
Multivariate (ฯ,ฮ)-modules by Gergely Zรกbrรกdi
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Find the value of the trigonometric expression using inverse
๐ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Multivariable Calculus - Part 8 - Gradient
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From playlist Multivariable Calculus
Multivariable Calculus - Part 8 - Gradient [dark version]
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From playlist Multivariable Calculus [dark version]
From playlist Probability Distributions
Multivariable Calculus - Part 9 - Geometric Picture of Gradient
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From playlist Multivariable Calculus
Multivariable Calculus - Part 9 - Geometric Picture for the Gradient [dark version]
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From playlist Multivariable Calculus [dark version]
Multivariable Calculus - Part 10 - Directional Derivative
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From playlist Multivariable Calculus
Multivariable Calculus - Part 10 - Directional Derivative [dark version]
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From playlist Multivariable Calculus [dark version]
Professor Mike West: Structured Dynamic Graphical Models & Scaling Multivariate Time Series
The Turing Lectures - Professor Mike West: Structured Dynamic Graphical Models & Scaling Multivariate Time Series. Click the below timestamps to navigate the video. 00:00:12 Welcome & Introduction by Doctor Ioanna Manolopoulou 00:01:19 Professor Mike West: Structured Dynamic
From playlist Turing Lectures
Eulerian Integral of the First Kind - Deriving the BETA FUNCTION! [ The non-trigonometric Version ]
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From playlist Integrals
Evaluating the composition of Functions
๐ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
From playlist Contributed talks One World Symposium 2020
Evaluating the composition of Functions
๐ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Evaluating the composition of Functions
๐ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Evaluating the composition of Functions
๐ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions