Assuming x is Real, how to get Mathematica to recognize the truth of this equation?
In[513]:= FullSimplify[Conjugate[DiracDelta[x]] == DiracDelta[x], x \[Element] Reals] Out[513]= Conjugate[DiracDelta[x]] == DiracDelta[x]
When x=0, DiracDelta[x] is not considered a number:
x=0
DiracDelta[x]
In[8]:= DiracDelta[0] // NumberQ Out[8]= False
Mathematica simplifies as you expect when x!=0:
x!=0
Simplify[Conjugate[DiracDelta[x]] == DiracDelta[x], x \[Element] Reals && x != 0]
Try ComplexExpand.
ComplexExpand
Thank you. That is helpful.
Thanks.
