Difference between revisions of "Gamma"

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(References)
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=References=
 
=References=
* {{BookReference|Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale|1895|Johann Heinrich Graf|prev=findme|next=findme}}: $\S 3. (15_a)$
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* {{BookReference|Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale|1895|Johann Heinrich Graf|prev=findme|next=findme}}: $\S 3 (15_a)$
 
* {{BookReference|A course of modern analysis|1920|Edmund Taylor Whittaker|author2=George Neville Watson|edpage=Third edition|prev=findme|next=Euler-Mascheroni constant}}: $\S 12 \cdot 1$
 
* {{BookReference|A course of modern analysis|1920|Edmund Taylor Whittaker|author2=George Neville Watson|edpage=Third edition|prev=findme|next=Euler-Mascheroni constant}}: $\S 12 \cdot 1$
 
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|next=Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0}}: §1.1 (1)
 
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|next=Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0}}: §1.1 (1)

Revision as of 16:16, 21 June 2016

The gamma function $\Gamma \colon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is the function initially defined for $\mathrm{Re}(z)>0$ by the integral by the formula $$\Gamma(x)=\displaystyle\int_0^{\infty} \xi^{x-1}e^{-\xi} \mathrm{d}\xi.$$ The analytic continuation of $\Gamma$ leads to a meromorphic function with poles at the negative integers.

Properties

Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0
Gamma function written as a limit of a factorial, exponential, and a rising factorial
Gamma function written as infinite product
Value of Gamma(1)
Factorial property of gamma
Gamma at positive integers
Relationship between Hurwitz zeta and gamma function
Gamma-Sine Relation
Bohr-Mollerup theorem

Videos

Gamma Function (playlist)
The Gamma Function: intro (5)
Gamma Integral Function - Introduction
Gamma function
Mod-04 Lec-09 Analytic continuation and the gamma function (Part I)
gamma function - Part 1
Beta Function, Gamma Function and their Properties
What's the Gamma Function?
euler gamma function
Thermodynamics 19 a : Gamma Function 1/2
The Gamma Function: why 0!=1 (5)
Gamma Function Of One-Half: Part 1
Gamma Function Of One-Half: Part 2
Gamma function at 1/2
Contour Integral Definition of the Gamma Function

See Also

Loggamma
Polygamma
Reciprocal gamma

References

The sine product formula and the gamma function
Leonhard Euler's Integral: A Historical Profile of the Gamma Function