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- Thread starter rmiller70015
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For [itex]x[/itex] noninteger (but the real part of x is greater than zero), you can define [itex]\Gamma(x)[/itex] by:

[itex]\Gamma(x) = \int_{t=0}^\infty e^{-t}t^{x-1} dt[/itex]

For the cases where the real part of [itex]x[/itex] is less than zero, you can define [itex]\Gamma(x)[/itex] by:

[itex]\Gamma(x) = \frac{\pi}{sin(\pi x) \Gamma(1-x)}[/itex]

So that defines [itex]\Gamma(x)[/itex] everywhere, except that it blows up at [itex]x=0, -1, -2, -3, ...[/itex]

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