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

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The discussion centers on the existence of a closed form formula for ln(x), with participants noting that a Taylor series can provide good approximations through term-by-term integration of 1/x. There is confusion regarding the notation, with "in(x)" being clarified as a typo for "ln(x)." Questions arise about the definition of a closed form and the allowable functions for such a formula. Additionally, it is highlighted that ln(x) has a singularity at x = 0, which complicates the use of Taylor series around that point. The conversation ultimately explores the limitations and possibilities of expressing ln(x) in a closed form.
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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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