In(x) Closed Form Formula: Does It Exist?

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Discussion Overview

The discussion revolves around the existence of a closed form formula for in(x), with participants exploring the implications of this question in the context of mathematical functions and series representations.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants inquire about the existence of a closed form formula for in(x), with one participant suggesting that the question may stem from a typographical error.
  • Another participant proposes that an arbitrarily good approximation of ln(x) can be achieved using the Taylor series representation by integrating term by term the sequence form of 1/x.
  • There is a concern raised about the singularity of ln(x) at x = 0, indicating that a Taylor series cannot be constructed around that point.
  • A participant questions what is meant by "closed formula" and asks about the functions that are permissible in this context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of a closed form for in(x), and multiple viewpoints regarding the nature of the question and the methods of approximation remain present.

Contextual Notes

Limitations include the ambiguity surrounding the definition of "closed formula" and the implications of singularities in the context of Taylor series expansions.

Topolfractal
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Does there exist a closed form formula for in(x)?
 
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You can get an arbitrarily good approximation with the Taylor series representation of ln(x) by integrating term by term the sequence form of 1/x.
 
Topolfractal said:
Does there exist a closed form formula for in(x)?
Typo? You have in instead of ln (lowercase "ell").
 
Mark44 said:
Typo? You have in instead of ln (lowercase "ell").
Ya In(x) is what I mean
 
Topolfractal said:
Does there exist a closed form formula for in(x)?

What do you mean with closed formula? What functions are you allowed to use?
 
Ln(x) has a singularity at x = 0, so you can't have a Taylor series around 0.
 

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