Generalized Functions

I would estimate your help.

Thanks a lot.

Hey mbempeni.

What definition do you have of a generalized function?

Thank you for your answer.

I mean Dirac δ function

Can you use the limiting function of the normal distribution (as variance goes to zero) to prove this?

@chiro
Can you explain what you mean? Thanks for your interest!

I mean the limiting formulation like these:

Dirac delta function - Wikipedia, the free encyclopedia

However I think a better way would be to use Laplace transforms to do this: have you used these before?

No, I haven 't.

Could you help me to solve it?

In laplace transforms you have the shift theorem which is referenced on the wiki site:

Laplace transform - Wikipedia, the free encyclopedia

Consider transforming both to Laplace space (frequency domain) and use the time-scaling and shift theorem to show that they are both equal Laplace transform functions.

Once you show that they are equal, then it follows that the functions are also equal.