Difference between revisions of "GammaFn"

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[[category:Analytic Distribution Functions]]
 
[[category:Analytic Distribution Functions]]
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= GammaFn(x) =
 
= GammaFn(x) =
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The gamma function grows very quickly, resulting in a numeric overflow when x>171.  The [[LGamma]] function computes the natural logarithm of the gamma function, and therefore can be used over much wider ranges.   
 
The gamma function grows very quickly, resulting in a numeric overflow when x>171.  The [[LGamma]] function computes the natural logarithm of the gamma function, and therefore can be used over much wider ranges.   
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The gamma function is defined as:
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:<math>\Gamma(x) = \int_0^{\infty} t^{x-1} e^{-t} dt</math>
  
 
= Library =
 
= Library =

Revision as of 21:01, 10 July 2007


GammaFn(x)

The complete gamma function.

One way to think of the gamma function is as a generalization of the Factorial function. Whereas, the factorial function has a range over the whole numbers, the Gamma function has a range over positive real numbers. The relationship between the gamma function and factorial is:

n! = GammaFn(n+1)

The gamma function grows very quickly, resulting in a numeric overflow when x>171. The LGamma function computes the natural logarithm of the gamma function, and therefore can be used over much wider ranges.

The gamma function is defined as:

[math]\displaystyle{ \Gamma(x) = \int_0^{\infty} t^{x-1} e^{-t} dt }[/math]

Library

Advanced Math

See Also

  • LGamma : Natural log of the gamma function.
  • GammaI : The incomplete gamma function.
  • Gamma : The gamma distribution
  • BetaFn : The complete beta function
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