Understanding a CRUX problem: visualizing using LogLinearPlot

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2

Great post,but:

Problem 1.

<< MaTex`
(*$Failed*)

Problem 2:

Integrate[Floor[Log[b, Floor[Ceiling[x]/x]]], {x, 0, Infinity}, Assumptions -> b > 1]
(*Integrate[Floor[Log[Floor[Ceiling[x]/x]]/Log[b]], {x, 0, \[Infinity]},
  Assumptions -> b > 0]*)(*Give me input*)

I executed this code on Mathematica 12.2.0.

3

  1. Please follow the link to install MaTeX and required packages. In general you do not need that to run the code because I only use it to display large formula and no computation depends on it.

  2. This is a very tricky integral with very specific strategy not included in automation. Typically breaking down domain for integration to (b^(k+1),b^k) is quite unusual and probably not used anywhere else

4

Mariusz,

For the first problem MaTeXInstall. Then

Needs["MaTeX`"]
5

Ok thanks.

6

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