..Hi,

is the following sequence of functions uniformly convergent for ?

whereas

is a constant

are constants

are constants

I think the pointwise limit is given by

Is this correct? Yes.

Does also converge uniformly to ? Uniform convergence is only defined if the domain of the functions is specified. If you want the variable a to run through the whole real line, then the convergence is not uniform. But I think that the functions will converge uniformly on any bounded interval.