# functions – Computing the sign of an expression

As $$sigma>0$$ we can divide the expression by $$sigma$$ without changing its sign. Then, defining $$x=(p-v_0)/sigma$$, the expression becomes

``````Sign(Sqrt(2) + E^(x^2/2)*Sqrt(π)*x*Erfc(-x/Sqrt(2)))
``````

This expression seems to be positive for any $$xinmathbb{R}$$, so I’d say that the answer to your question is that your `Sign(...)` is always 1:

``````LogPlot(Sqrt(2) + E^(x^2/2)*Sqrt(π)*x*Erfc(-x/Sqrt(2)), {x, -1000, 10},
WorkingPrecision -> 100, PlotRange -> All)
``````

The asymptotes of your expression are

• $$sqrt{2}/x^2$$ for $$xto-infty$$, which is positive,
• $$2xsqrt{pi} e^{frac{x^2}{2}}$$ for $$xto+infty$$, which is positive.