# What do vertical bars with an index mean?

A fairly basic notation question: what do the vertical bars in the following mean?

x = $_{k=0}^{3}\big|\;f(k)\;\big|$

I've never seen vertical bars with an index before and I can't seem to find the answer on google either (half the problem is that I don't know what I'm looking for!).

Encountered on page 3, equations 3-7 in this research paper. The most sensible interpretation I can think of is sum then take the absolute value.

• Looks like a formatting error to me. Equation (2) on pg. 1 has half a right-floor bracket missing, so it's quite conceivable there's supposed to be a $\sum$ where the blank space is. The overly-large italicized A also seems a bit out of place. – Erick Wong Mar 13 '14 at 20:34
• Thanks, I suspect you are right. – sjmeverett Mar 13 '14 at 20:46

## 1 Answer

It definitely looks like a $\sum$ is missing. You are supposed to sum up the four terms with $k$ running from $0$ to $3$, then take the absolute value. The sum indices then should be inside the absolute value signs.

• For completeness I'd like to add that it would appear they actually meant $\big|\sum_{k=0}^{3}\;f(k)\;\big|$ because it makes much more sense in the particular context. – sjmeverett Mar 13 '14 at 21:16
• @stewartml: looking at it again, I agree. Fixed – Ross Millikan Mar 13 '14 at 21:19