# Blanking on word for kind of convergence of a sum

by Office_Shredder
Tags: blanking, convergence, kind, word
 Emeritus Sci Advisor PF Gold P: 4,500 I have a sum $$\sum_{n=-\infty}^{\infty} f(n)$$ which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit $$\lim_{N\to \infty} \sum_{n=-N}^{N} f(n).$$ I know that when this limit exists the sum is _____ convergent, or is a _____ sum, where _____ is something like principal, or first order, or perhaps a name like a Dirichlet sum (I'm making these up of course). Does anybody know what the word I am looking for is?
 Mentor P: 18,026 Seems like you want the (Cauchy) principal value of the series. This is a well-known thing for integrals, but I've seen the term used for series too.
Emeritus
PF Gold
P: 4,500
 Quote by micromass Seems like you want the (Cauchy) principal value of the series. This is a well-known thing for integrals, but I've seen the term used for series too.
That is exactly the term I was looking for. See, I knew the word principal was involved somehow

P: 1,666
Blanking on word for kind of convergence of a sum

 Quote by Office_Shredder Does anybody know what the word I am looking for is?
Fourier.

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