My Math Forum PROBLEM IN GAMA FUNCTION

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 December 26th, 2010, 02:59 AM #1 Newbie   Joined: Dec 2010 Posts: 11 Thanks: 0 PROBLEM IN GAMA FUNCTION [color=#FF8000]Hello good mathematician your forum is very useful[/color] [color=#FF4000] i bigin my poroblem : prove that[/color] $\Gamma (n)= \int\limits_0^\infty {\mathop {\left( {\ln \frac{1}{x}} \right)}\nolimits^{n - 1} dx}$ [color=#0000FF]I hope it is solved soon[/color] Note: [color=#FF0000]I have written this equestion by latex in a forum ,the bracket [\mathop?] was not finding.that means the problem in this forum[/color]!!!
 December 26th, 2010, 09:12 AM #2 Newbie   Joined: Dec 2010 Posts: 11 Thanks: 0 Re: PROBLEM IN GAMA FUNCTION [color=#4000FF]i try solve it: from dfine of gama[/color] $\Gamma n= \int\limits_0^\infty {\mathop y\nolimits^{n - 1} \mathop e\nolimits^{ - y} dy}$ .....1 [color=#4000FF]let [/color] $y= \ln \frac{1}{x}$ .................................................. .......................................2 $x= \mathop e\nolimits^{ - y}$ .................................................. ....................3 $dx= - \mathop e\nolimits^{ - y} dy$.................................................. ..............4 [color=#0000FF]then[/color] $\int\limits_0^\infty {\mathop {\left( {\ln \frac{1}{x}} \right)}\nolimits^{n - 1}= - \int\limits_0^\infty {\mathop y\nolimits^{n - 1} } \mathop e\nolimits^{ - y} }$ [color=#FF4000]what is the broblem of (-) ? i think from intigral look to the equetion[/color] 3

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