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Convergence in Euler-Maclaurin
The Next CEO of Stack OverflowEuler-Maclaurin summation for $e^-x^2$help with an asymptotic for a certain productEuler-Maclaurin SummationHow to estimate $ left(1 + sqrt2 + sqrt3 + dots + sqrtn right) - frac23 n sqrtn$?Can you give a closed form or an asymptotic for $sum_m=0^k-1cos(frac2pi m nk log 2)$ for $ktoinfty$?Criteria for formally derived Euler-Maclaurin-type formulaDistinction between finite and infinite Taylor series.When do Taylor series converge quickly?Differentiation Error TermEuler-Maclaurin Formula Definition Confusion
$begingroup$
In the Euler-Maclaurin formula, we get an asymptotic approximation with the error term arbitrary small. However, I am confused about the convergence. The problem is that the constants in the terms grow really quickly, which means that it will not necessarily converge.
Well, it doesn't sound very useful to have an asymptotic approximation that does not converge. However, in practice, it seems to give a really good approximation, despite the growing constants. There really must be something I am missing. But what?
real-analysis analysis summation euler-maclaurin
asked Mar 20 at 10:20
user2316602user2316602
707
$endgroup$
add a comment |
$begingroup$
In the Euler-Maclaurin formula, we get an asymptotic approximation with the error term arbitrary small. However, I am confused about the convergence. The problem is that the constants in the terms grow really quickly, which means that it will not necessarily converge.
Well, it doesn't sound very useful to have an asymptotic approximation that does not converge. However, in practice, it seems to give a really good approximation, despite the growing constants. There really must be something I am missing. But what?
real-analysis analysis summation euler-maclaurin
asked Mar 20 at 10:20
user2316602user2316602
707
$endgroup$
add a comment |
$begingroup$
In the Euler-Maclaurin formula, we get an asymptotic approximation with the error term arbitrary small. However, I am confused about the convergence. The problem is that the constants in the terms grow really quickly, which means that it will not necessarily converge.
Well, it doesn't sound very useful to have an asymptotic approximation that does not converge. However, in practice, it seems to give a really good approximation, despite the growing constants. There really must be something I am missing. But what?
real-analysis analysis summation euler-maclaurin
asked Mar 20 at 10:20
user2316602user2316602
707
$endgroup$
In the Euler-Maclaurin formula, we get an asymptotic approximation with the error term arbitrary small. However, I am confused about the convergence. The problem is that the constants in the terms grow really quickly, which means that it will not necessarily converge.
Well, it doesn't sound very useful to have an asymptotic approximation that does not converge. However, in practice, it seems to give a really good approximation, despite the growing constants. There really must be something I am missing. But what?
real-analysis analysis summation euler-maclaurin
real-analysis analysis summation euler-maclaurin
asked Mar 20 at 10:20
user2316602user2316602
707
asked Mar 20 at 10:20
user2316602user2316602
707
asked Mar 20 at 10:20
user2316602user2316602
707
asked Mar 20 at 10:20
user2316602user2316602
707
asked Mar 20 at 10:20
user2316602user2316602
707
707
add a comment |
add a comment |
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