Editing Gamma function (section)

=== Particular values ===
{{Main|Particular values of the gamma function}}
Including up to the first 20 digits after the decimal point, some particular values of the gamma function are:
<math display="block">\begin{array}{rcccl}
\Gamma\left(-\tfrac{3}{2}\right) &=& \tfrac{4\sqrt{\pi}}{3} &\approx& +2.36327\,18012\,07354\,70306 \\
\Gamma\left(-\tfrac{1}{2}\right) &=& -2\sqrt{\pi} &\approx& -3.54490\,77018\,11032\,05459 \\
\Gamma\left(\tfrac{1}{2}\right) &=& \sqrt{\pi} &\approx& +1.77245\,38509\,05516\,02729 \\
\Gamma(1) &=& 0! &=& +1 \\
\Gamma\left(\tfrac{3}{2}\right) &=& \tfrac{\sqrt{\pi}}{2} &\approx& +0.88622\,69254\,52758\,01364 \\
\Gamma(2) &=& 1! &=& +1 \\
\Gamma\left(\tfrac{5}{2}\right) &=& \tfrac{3\sqrt{\pi}}{4} &\approx& +1.32934\,03881\,79137\,02047 \\
\Gamma(3) &=& 2! &=& +2 \\
\Gamma\left(\tfrac{7}{2}\right) &=& \tfrac{15\sqrt{\pi}}{8} &\approx& +3.32335\,09704\,47842\,55118 \\
\Gamma(4) &=& 3! &=& +6
\end{array}</math>
(These numbers can be found in the [[On-Line Encyclopedia of Integer Sequences|OEIS]].<ref>{{Cite OEIS|A245886|Decimal expansion of Gamma(-3/2), where Gamma is Euler's gamma function}}</ref><ref>{{Cite OEIS|A019707|Decimal expansion of sqrt(Pi)/5}}</ref><ref>{{Cite OEIS|A002161|Decimal expansion of square root of Pi}}</ref><ref>{{Cite OEIS|A019704|Decimal expansion of sqrt(Pi)/2}}</ref><ref>{{Cite OEIS|A245884|Decimal expansion of Gamma(5/2), where Gamma is Euler's gamma function}}</ref><ref>{{Cite OEIS|A245885|Decimal expansion of Gamma(7/2), where Gamma is Euler's gamma function}}</ref> The values presented here are truncated rather than rounded.)
The complex-valued gamma function is undefined for non-positive integers, but in these cases the value can be defined in the [[Riemann sphere]] as {{math|∞}}. The [[reciprocal gamma function]] is [[well defined]] and [[analytic function|analytic]] at these values (and in the [[entire function|entire complex plane]]):
<math display="block">\frac{1}{\Gamma(-3)} = \frac{1}{\Gamma(-2)} = \frac{1}{\Gamma(-1)} = \frac{1}{\Gamma(0)} = 0.</math>