Cfrgtkky

7 1 $begingroup$ I have a simple gaussian integral: $int^{infty}_{-infty}dx:e^{ialpha x^2}$ . If $alpha in mathbb{R}$ , then: $$ int^infty_{-infty} dx; e^{i , alpha x^2} = sqrt{frac pi {-i alpha}} qquad qquad alpha <0 $$ Now if $alpha in mathbb{C}$ then we obtain the same answer but with different conditions: $$ int^infty_{-infty} dx; e^{i , alpha x^2} = sqrt{frac pi {-i alpha}} qquad qquad Im(alpha)>0 $$ These can be combined into a simple answer with an OR statement: $$ int^infty_{-infty} dx; e^{i , alpha x^2} = sqrt{frac pi {-i alpha}} qquad qquad Im(alpha)=0 , & , Re(alpha) <0 quad|| quad Im(alpha)>0 $$ When I I ask Mathematica to solve this for me Integrate[E^(I x^2 a), {x, -∞, ∞}] Mathematica returns only one of these cases: ConditionalExpression[Sqrt[π]/Sqrt[-I a