Difference between revisions of "Manuals/calci/GAMMAFUNCTION"

Latest revision as of 03:55, 12 August 2020

GAMMAFUNCTION (z)

This function gives the value of the Gamma function.
The Gamma function is defined to be an extension of the factorial to complex and real number arguments.
That is, if n is a positive integer:

$\Gamma (n)=(n-1)!$

Gamma function is defined for all complex numbers except the non-positive integers.
For complex numbers with a positive real part, it is defined via a convergent improper integral:

$\Gamma (z)=\int \limits _{0}^{\infty }x^{z-1}e^{-x}dx$

This function will return the result as NaN when the given number as negative or Non numeric.

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-==gamma==
+<div style="font-size:30px">'''GAMMAFUNCTION (z)'''</div><br/>
+*<math>z</math> is any positive real number.
+==Description==
+*This function gives the value of the Gamma function.
+*The Gamma function is defined to be an extension of the factorial to complex and real number arguments.
+*That is, if n is a positive integer:
+<math>\Gamma (n)=(n-1)!</math>
+*Gamma function is defined for all complex numbers except the non-positive integers.
+*For complex numbers with a positive real part, it is defined via a convergent improper integral:
+<math>\Gamma (z) = \int\limits_{0}^{\infty} x^{z-1} e^{-x} dx </math>
+*This function will return the result as NaN when the given number as negative or Non numeric.
+==Examples==
+#GAMMAFUNCTION(2) = 1.0000026676984093
+#GAMMAFUNCTION(45.3) = 8.308990531109891e+54
+#GAMMAFUNCTION(-3) = #N/A (#NUM!)
+==Related Videos==
+{{#ev:youtube|v=XZIVrkkYBRI|280|center|Gamma Function}}
+==See Also==
+*[[Manuals/calci/GAMMADIST | GAMMADIST]]
+*[[Manuals/calci/SUM  | SUM ]]
+==References==
+*[https://en.wikipedia.org/wiki/Gamma_function Gamma Function]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]