Mathematica Understanding Gamma(x) Function

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The gamma function, denoted as gamma(x), is a mathematical function defined for complex numbers that generalizes the factorial function. For positive integers, it satisfies the relationship gamma(n) = (n-1)!, linking it directly to factorials. The gamma function can be expressed as an integral for certain arguments and adheres to specific functional equations. It also has poles at negative integers. Additional information about the gamma function can be found on resources like MathWorld. The discussion highlights the function's significance and its applications in mathematics.
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Can anyone explain to me, in as simple a way as possible, what the math functoin "gamma(x)" does. I am very curious, and would appreciate any help that can be given.
 
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It is a function defined on the complex numbers that satisfies \Gamma(n)=(n-1)! for integer n and is treated as a generalization of factorials. It has, for certain arguments, got a nice expression as a integral; it satisifes certain functional equations; there are poles at the negative integers; lots more information can be found at
http://mathworld.wolfram.com/GammaFunction.html
 
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Thank you for the information, matt grime, it was very helpful. I hope that maby I can help you in the future.
 

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