What does a ellipsis directly following a summation mean?

In summary, the notation in equation \ref{aixi_eq} represents a string of summations with a variable $k$ ranging from 0 to $m$ and a variable $t$ being incremented. It also involves maximizing a function and summing over all possible outcomes and rewards. The final term represents a probability calculation based on a set of conditions.
  • #1
ektrules
35
0
I've never seen this notation before. What does the ellipsis right after the first summation mean:
[tex]\begin{equation}
\label{aixi_eq}
a_t^* = \arg\max\limits_{a_t}\sum\limits_{o_t r_t} \dots \max\limits_{a_{t+m}}\sum\limits_{o_{t+m} r_{t+m}}[r_t + \dots + r_{t+m}]
\sum\limits_{q:U(q,a_1...a_{t+m})=o_1 r_1 ... o_{t+m}r_{t+m}}2^{-\ell(q)}.
\end{equation}[/tex]
 
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  • #2
My guess: a string of summations with at+k with 0<k<m.
 
  • #3
mathman said:
My guess: a string of summations with at+k with 0<k<m.

That's it, thanks.
 

What does a ellipsis directly following a summation mean?

An ellipsis directly following a summation indicates that the summation continues infinitely, and the ellipsis is used to show that there are terms that have been left out.

How do I interpret an ellipsis following a summation?

When an ellipsis is used after a summation, it means that the series or sequence extends to infinity and the ellipsis is used to indicate that there are terms that have not been explicitly written out.

Why is an ellipsis used after a summation?

The use of an ellipsis after a summation is to indicate that there are infinitely many terms that have not been listed out, and to avoid writing out an infinite number of terms in a finite space.

Can an ellipsis following a summation be used in other contexts?

Yes, an ellipsis can be used after a summation in other contexts such as in mathematical proofs, where it can indicate that there are further steps or terms that have not been explicitly written out.

How do I know when to use an ellipsis after a summation?

An ellipsis is typically used after a summation when the series or sequence extends to infinity, and there is a need to indicate that there are terms that have not been explicitly listed out.

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