Editing Gamma function (section)

=== Extension to negative, non-integer values ===
Although the main definition of the gamma function&mdash;the Euler integral of the second kind&mdash;is only valid (on the real axis) for positive arguments, its domain can be extended with [[analytic continuation]]<ref>{{cite book |last1=Oldham |first1=Keith |last2=Myland |first2=Jan |last3=Spanier |first3=Jerome |title=An Atlas of Functions |date=2010 |publisher=Springer Science & Business Media |location=Ch 43 |isbn=9780387488073 |edition=2}}</ref> to negative arguments by shifting the negative argument to positive values by using either the Euler's reflection formula,
<math display="block">
\Gamma(-x) = \frac{1}{\Gamma(x+1)}\frac{\pi}{\sin\big(\pi(x+1)\big)},
</math>
or the fundamental property,
<math display="block">
\Gamma(-x):=\frac1{-x}\Gamma(-x+1) ,
</math>
when <math>x\not\in\mathbb{Z}</math>. 
For example,
<math display="block">
\Gamma\left(-\frac12\right)=-2\Gamma\left(\frac12\right) .
</math>