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Blanking on word for kind of convergence of a sum

by Office_Shredder
Tags: blanking, convergence, kind, word
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Office_Shredder
#1
Sep19-13, 05:43 PM
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I have a sum
[tex] \sum_{n=-\infty}^{\infty} f(n) [/tex]
which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit
[tex] \lim_{N\to \infty} \sum_{n=-N}^{N} f(n). [/tex]

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?
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micromass
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Sep19-13, 05:54 PM
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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.
Office_Shredder
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Sep19-13, 05:58 PM
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Quote Quote by micromass View Post
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

jackmell
#4
Sep21-13, 07:17 AM
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Blanking on word for kind of convergence of a sum

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


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