# [✓] Account for this non-odd result from FourierSinTransform?

GROUPS:
 The docs state The Fourier sine transform of a function f(t) is by default defined to be Sqrt[2/\[Pi]]\!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$\[Infinity]$$]$$\(f(t)$$\ $$sin(\[Omega] t)$$ d t\)\). It's easier viewed here: http://reference.wolfram.com/language/ref/FourierSinTransform.htmlOn the right side of the definition, the variable omega appears only as a factor inside Sin, and Sin is an odd function, so any function returned by FourierSinTransform should be an odd function.However, Mathematica returns a non-odd function on FourierSinTransform of ArcTan: In[4]:= FourierSinTransform[ArcTan[t], t, \[Omega]] Out[4]= (E^-\[Omega] Sqrt[\[Pi]/2])/\[Omega] Also easier to view in the docs, where it's given as an example.The docs also state "Results from FourierSinTransform and FourierTransform differ by a factor of I for odd functions". That's how it should be, but that's not how it really is when they're applied to ArcTan.