Difference between revisions of "GammaFn"
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[[category:Analytic Distribution Functions]] | [[category:Analytic Distribution Functions]] | ||
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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: | ||
+ | :<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
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