I started looking at a proof I had set aside for myself to read some time ago* and wondered if I was missing something in the notation.(adsbygoogle = window.adsbygoogle || []).push({});

In several of the author's formulas, he writes [tex]\ln_2k[/tex]. Is this just [tex]\log_2k=\lg k[/tex]?

On a related note, since I see this as well: I've seen notation of the form [tex]f^k[/tex] used in two different ways -- [tex]f^k(x)=f(x)\cdot f^{k-1}(x)[/tex] (usually trig functions or logs) and [tex]f^k(x)=f(f^{k-1}(x))[/tex] (usually number-theoretic functions like [tex]\sigma[/tex], but I suppose function inverses are like this in a sense). Is there any rhyme or reason behind the choice to use one or the other as convention? Is one gaining popularity with respect to the other over time?

* Pierre Dusart, "The kth Prime is Greater than [tex]k(\ln k+\ln\ln k-1)[/tex] for [tex]k\geq2[/tex]", Math. Comp. 68/225 Jan 1999, pp. 411-415.

Edit: I'm such a fool. The author does define it after all, I just missed it in my carelessness. [tex]\ln_2k=\ln\ln k[/tex] in this paper.

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# Notation: ln_2(k)?

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