The name of x^n/(x^2+a^2)

What is the name and inner mathematical/physical significance of the
function 'f(x)=x^n/(x^2+a^2)' when n=1? ('a' a constant)

n=0 is a Lorentzian and n=2 is a Fano shape. n=1 occurs, for instance, as
the imaginary part in the Lorentz oscillator spectrum. In the end, has this
function/structure/shape a name and a compelling meaning?

Regards,

F.P.L.

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