Asymptotics of $f(z)$ where $z=int_2^{f(z)} frac{dx}{ln(x)}$
$begingroup$
I am trying to determine what the behavior of the inverse logarithmic integral is as $zto infty$. I noticed that $f'(z)=ln(f(z))$ which follows from differentiating $$z=int_2^{f(z)} frac{dx}{ln(x)}$$ but I do not know if that could help in this situation. If anyone has any ideas or methods on how to find the asymptotics of this function it would be greatly appreciated.
logarithms asymptotics
asked Jan 9 at 21:21
aledenaleden
2,027511
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add a comment |
$begingroup$
I am trying to determine what the behavior of the inverse logarithmic integral is as $zto infty$. I noticed that $f'(z)=ln(f(z))$ which follows from differentiating $$z=int_2^{f(z)} frac{dx}{ln(x)}$$ but I do not know if that could help in this situation. If anyone has any ideas or methods on how to find the asymptotics of this function it would be greatly appreciated.
logarithms asymptotics
asked Jan 9 at 21:21
aledenaleden
2,027511
$endgroup$
add a comment |
$begingroup$
I am trying to determine what the behavior of the inverse logarithmic integral is as $zto infty$. I noticed that $f'(z)=ln(f(z))$ which follows from differentiating $$z=int_2^{f(z)} frac{dx}{ln(x)}$$ but I do not know if that could help in this situation. If anyone has any ideas or methods on how to find the asymptotics of this function it would be greatly appreciated.
logarithms asymptotics
asked Jan 9 at 21:21
aledenaleden
2,027511
$endgroup$
I am trying to determine what the behavior of the inverse logarithmic integral is as $zto infty$. I noticed that $f'(z)=ln(f(z))$ which follows from differentiating $$z=int_2^{f(z)} frac{dx}{ln(x)}$$ but I do not know if that could help in this situation. If anyone has any ideas or methods on how to find the asymptotics of this function it would be greatly appreciated.
logarithms asymptotics
logarithms asymptotics
asked Jan 9 at 21:21
aledenaleden
2,027511
asked Jan 9 at 21:21
aledenaleden
2,027511
asked Jan 9 at 21:21
aledenaleden
2,027511
asked Jan 9 at 21:21
aledenaleden
2,027511
asked Jan 9 at 21:21
aledenaleden
2,027511
2,027511
add a comment |
add a comment |
1 Answer
1
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$begingroup$
Since
$int_2^{z} frac{dx}{ln(x)}
$
is essentially the
logarithmic integral
(see https://en.wikipedia.org/wiki/Logarithmic_integral_function),
what you are looking for is the
inverse of this.
A search for
"inverse of logarithmic integral"
comes up with a number of good hits
including this,
here:
Inverse logarithmic integral
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Since
$int_2^{z} frac{dx}{ln(x)}
$
is essentially the
logarithmic integral
(see https://en.wikipedia.org/wiki/Logarithmic_integral_function),
what you are looking for is the
inverse of this.
A search for
"inverse of logarithmic integral"
comes up with a number of good hits
including this,
here:
Inverse logarithmic integral
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
$endgroup$
add a comment |
$begingroup$
Since
$int_2^{z} frac{dx}{ln(x)}
$
is essentially the
logarithmic integral
(see https://en.wikipedia.org/wiki/Logarithmic_integral_function),
what you are looking for is the
inverse of this.
A search for
"inverse of logarithmic integral"
comes up with a number of good hits
including this,
here:
Inverse logarithmic integral
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
$endgroup$
add a comment |
$begingroup$
Since
$int_2^{z} frac{dx}{ln(x)}
$
is essentially the
logarithmic integral
(see https://en.wikipedia.org/wiki/Logarithmic_integral_function),
what you are looking for is the
inverse of this.
A search for
"inverse of logarithmic integral"
comes up with a number of good hits
including this,
here:
Inverse logarithmic integral
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
$endgroup$
Since
$int_2^{z} frac{dx}{ln(x)}
$
is essentially the
logarithmic integral
(see https://en.wikipedia.org/wiki/Logarithmic_integral_function),
what you are looking for is the
inverse of this.
A search for
"inverse of logarithmic integral"
comes up with a number of good hits
including this,
here:
Inverse logarithmic integral
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
answered Jan 10 at 0:01
marty cohenmarty cohen
73.1k549128
73.1k549128
add a comment |
add a comment |
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