I recently managed to analytically continue certain divergent series. I was hoping if anyone could tell me if they appeared somewhere in physics:
limk→∞limn→∞(n∑r=1r−2s+1f(krn)kn)=limj→1ζ(j)ζ(−2s+1−j)⏟removable singularity∫∞0f(x)dx
For those interested in the derivation I uploaded it on dropbox (section
3.2):
Derivation