Dirac (delta) function

The delta "function" isn't an ordinary function; it's a distribution, and it only makes sense when you integrate it. It's *defined* by the property
[tex]\int_{-\infty}^\infty \delta(x) f(x) \;dx = f(0)[/tex]
for suitable test functions [itex]f[/itex].

 

In other words, the delta function is the operator that maps f(x) to f(0).

This doesn't belong in this area. I am moving it to "Calculus and Analysis"

 

Look for a textbook that sounds like "Distribution theory" and you'll find what you need.

 

If you wish to understand what the Dirac delta "really is", and how it might be represented as a sort of "limit", then you may read the following tutorial:
https://www.physicsforums.com/showthread.php?t=73447

 

arilno, that link is invalid.

 

I've fixed it now.