- Examples
- Oscillatory integral
- See also
- References
In mathematics, distributional calculus is a generalized form of calculus that is based on the notion of distributions (generalized function), as opposed to classical calculus, which is based on functions.
Examples
A distributional limit may still exist when the classical limit doesn't. Consider, for example, the function:
Since, by integration by parts,
we have: 
. That is, the limit of 
as 
is 
.
Let 
denote the distributional limit of 
as 
, if it exists. The distribution 
is defined similarly.
One has
Let 
be the rectangle with positive orientation, with an integer N. By the residue formula,
On the other hand,
See also: dipole.
Oscillatory integral
{{main|Oscillatory integral}}See also
- Distribution (number theory)
References
- Demailly, Complex Analytic and Differential Geometry
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