a[k_]:=1/(Abs[k]^2+1)b[k_]:=Exp[-k^2]S
Table[a[k],{k,-4,4}]
Out[]=
,,,,1,,,,
1
5
1
4
1
3
1
2
1
2
1
3
1
4
1
5
ListPlot[Table[b[k],{k,-10,10}]]
Out[]=
NSum[b[k],{k,-Infinity,Infinity}]
Out[]=
1.77264
Table[{n,NSum[a[k]b[n-k],{k,-Infinity,Infinity}]},{n,-10,10}]//TableForm
Out[]//TableForm=
-10 | 0.017814 |
-9 | 0.0220178 |
-8 | 0.0279107 |
-7 | 0.0365387 |
-6 | 0.0499069 |
-5 | 0.0722687 |
-4 | 0.113983 |
-3 | 0.205205 |
-2 | 0.440187 |
-1 | 0.952477 |
0 | 1.37523 |
1 | 0.952477 |
2 | 0.440187 |
3 | 0.205205 |
4 | 0.113983 |
5 | 0.0722687 |
6 | 0.0499069 |
7 | 0.0365387 |
8 | 0.0279107 |
9 | 0.0220178 |
10 | 0.017814 |