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Blanking on word for kind of convergence of a sum 
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#1
Sep1913, 05:43 PM

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Sci Advisor
PF Gold
P: 4,500

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? 


#2
Sep1913, 05:54 PM

Mentor
P: 18,331

Seems like you want the (Cauchy) principal value of the series. This is a wellknown thing for integrals, but I've seen the term used for series too.



#3
Sep1913, 05:58 PM

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PF Gold
P: 4,500




#4
Sep2113, 07:17 AM

P: 1,666

Blanking on word for kind of convergence of a sum



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