Editing Imaginary unit (section)

=== Factorial ===
The [[factorial]] of the imaginary unit {{mvar|i}} is most often given in terms of the [[gamma function]] evaluated at {{math|1 + ''i''}}:<ref>{{cite journal |last1=Ivan |first1=M. |last2=Thornber |first2=N. |last3=Kouba |first3=O. |last4=Constales |first4=D. |title=Arggh! Eye factorial . . . Arg(i!) |journal=[[American Mathematical Monthly]] |volume=120|pages=662–665  |year=2013 |issue=7 |doi=10.4169/amer.math.monthly.120.07.660|s2cid=24405635 }} {{pb}} [[Neil_Sloane|Sloane, N. J. A.]] (ed.).  "Decimal expansion of the real part of i!", Sequence {{OEIS link|A212877}}; and "Decimal expansion of the negated imaginary part of i!", Sequence {{OEIS link|A212878}}. ''The [[On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation.</ref>

<math display=block>i! = \Gamma(1+i) = i\Gamma(i) \approx 0.4980 - 0.1549\,i.</math>

The magnitude and argument of this number are:<ref>[[Neil_Sloane|Sloane, N. J. A.]] (ed.).  "Decimal expansion of the absolute value of i!", Sequence {{OEIS link|A212879}}; and "Decimal expansion of the negated argument of i!", Sequence {{OEIS link|A212880}}. ''The [[On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation.</ref>

<math display=block>
|\Gamma(1+i)| = \sqrt{\frac{\pi}{ \sinh \pi}} \approx 0.5216, \quad
\arg{\Gamma(1+i)} \approx -0.3016.
</math>