Difference between revisions of "Gamma"

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* {{BookReference|Special Functions|1960|Earl David Rainville|prev=findme|next=findme}}: $15.(1)$
 
* {{BookReference|Special Functions|1960|Earl David Rainville|prev=findme|next=findme}}: $15.(1)$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Gauss' formula for gamma function}}: $6.1.1$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Gauss' formula for gamma function}}: $6.1.1$
* {{BookReference|The Special Functions And Their Approximations, Volume I|1969|Yudell L. Luke|next=findme}} $(1)$
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* {{BookReference|The Special Functions And Their Approximations, Volume I|1969|Yudell L. Luke|prev=findme|next=findme}} $2.1 (1)$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 01:54, 30 May 2017

The gamma function $\Gamma \colon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is the function initially defined for $x>0$ 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

What's the Gamma Function? (16 September 2008)
Gamma Function Of One-Half: Part 1 (10 August 2010)
Gamma Function Of One-Half: Part 2 (10 August 2010)
Gamma Integral Function - Introduction (5 December 2011)
gamma function - Part 1 (9 February 2012)
Gamma Function (playlist) (26 February 2012)
Gamma function (20 October 2012)
Beta Function, Gamma Function and their Properties (17 August 2013)
Thermodynamics 19 a : Gamma Function 1/2 (31 August 2013)
euler gamma function (14 September 2013)
The Gamma Function: intro (5) (13 February 2014)
The Gamma Function: why 0!=1 (5) (13 February 2014)
Mod-04 Lec-09 Analytic continuation and the gamma function (Part I) (3 June 2014)
Gamma function at 1/2 (3 January 2015)
Contour Integral Definition of the Gamma Function (18 January 2015)

External links

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

See Also

Loggamma
Polygamma
Reciprocal gamma

References