I'm an engineer and recently, within my work on non uniform signal sampling, I encountered the following series :
with , and all positive constants.
As can be seen, the series is a sum of normal distributions with means equal to and variances equal to
I found numerically (using Matlab) that the limit of as tends to is amazingly equal to .
I tried to proof this interesting result but with no success yet.
If anybody could help me, I'd be grateful to him...
Thanks for any help,