- #1
poonintoon
- 17
- 0
Hopefully people are still prowling the forums this close to christmas :)
I want to show that sin(ax)/x is a representation of a delta function in the limit a->infinty i.e
1) It equals 0 unless x=0
2) integrated from plus minus infinity it equals 1 and
3) multiplying by an arbitrary function f(x) and integrating gives f(0)
but I cannot show any of these. I have tried series representation, writing out as exponentials, looking up definite integrals etc but cannot make any headway.
Cheers
I want to show that sin(ax)/x is a representation of a delta function in the limit a->infinty i.e
1) It equals 0 unless x=0
2) integrated from plus minus infinity it equals 1 and
3) multiplying by an arbitrary function f(x) and integrating gives f(0)
but I cannot show any of these. I have tried series representation, writing out as exponentials, looking up definite integrals etc but cannot make any headway.
Cheers