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

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SUMMARY

The discussion centers on the existence of a closed form formula for the natural logarithm function, ln(x). Participants clarify that the Taylor series representation of ln(x) can provide approximations, but it cannot be centered around x = 0 due to the singularity at that point. The conversation emphasizes the importance of understanding the limitations of Taylor series in relation to ln(x) and the need for clarity in terminology, particularly distinguishing between "in(x)" and "ln(x)".

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  • Understanding of Taylor series and their applications
  • Familiarity with the natural logarithm function, ln(x)
  • Knowledge of singularities in mathematical functions
  • Basic calculus concepts, particularly integration
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  • Research the Taylor series expansion of ln(x) and its convergence properties
  • Explore the implications of singularities in mathematical analysis
  • Investigate alternative series representations for ln(x) around different points
  • Learn about numerical methods for approximating logarithmic functions
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Mathematicians, students studying calculus, and anyone interested in the properties of logarithmic functions and series approximations.

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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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