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I am reading a paper (to be able to implement the Baum-Welch algorithm in it) and the following notation is defined:

$$ [ a_k ]_{k=i}^j ≡ (a_i, a_{i+1}, \ldots , a_j) $$

$$ [a(k)]_{k=i}^j ≡ (a(i), a(i+ 1), \ldots , a( j)) $$

I (think) the first is shorthand of a n-tuple. I guess the second is something like that, but I don't understand the difference between the first and the second. Is this common notation something odd, or what? I am pretty rusty on my math, so if I am missing something obvious please don't hesitate to point that out.

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    They're the same – just that one uses subscript notation and another uses function notation.2012-05-17
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    Thanks! Any idea why you would bother to differentiate?2012-05-17
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    Sometimes you want to emphasize the fact that $a$ is a function of $k$. Sometimes the choice is made on the basis of readability: one version combines badly with other notation in use, resulting in cluttered expressions that are hard to read. Sometimes you just happened to use one instead of the other.2012-05-17
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    I am not sure [tag:markov-chains] is appropriate here. I'm also not sure about another tag2012-05-17

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