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Staff Picks Mathematics Calculus Discrete Mathematics Graphics and Visualization Wolfram Language Computer-Based Maths

Understanding a CRUX problem: visualizing using LogLinearPlot

Shenghui Yang

Shenghui Yang, WOLFRAM

Posted 4 years ago

POSTED BY: Shenghui Yang

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EDITORIAL BOARD

EDITORIAL BOARD, WOLFRAM

Posted 4 years ago

-- you have earned *Featured Contributor Badge* Your exceptional post has been selected for our editorial column *Staff Picks* http://wolfr.am/StaffPicks and Your Profile is now distinguished by a *Featured Contributor Badge* and is displayed on the Featured Contributor Board. Thank you!

POSTED BY: EDITORIAL BOARD

Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 4 years ago

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.

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.

POSTED BY: Mariusz Iwaniuk

Shenghui Yang

Shenghui Yang, WOLFRAM

Posted 4 years ago

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. 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