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Results tagged with sequences-and-series
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user 9404
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
1
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3
answers
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Inverting a power series? ... Cornish Fisher
Hello
In the derivation of the cornish fisher expansion, the following equation is obtained:
$$
\sum_{n=2}^{\infty} b_n H_{n-1}(x_\alpha) = \sum_{j=1}^{\infty}\frac{(x_\alpha - z_\alpha)^j}{j!}H_{j- …
- 579
5
votes
2
answers
785
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Inverting an asymptotic series
I have the first few terms of a series of the form,
$y(x)=\ln(x)+x+a_0+\frac{a_1}{x}+\frac{a_2}{x^2}+\cdots$.
Knowing that the inverse $x(y)$ exists, I am looking for method to write x in terms of …
- 579
30
votes
2
answers
16k
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power series of the reciprocal... does a recursive formula exist for the coefficients [closed]
Let $f(x)=\sum _{n=0}^{\infty } b_nx^n$ and $\frac{1}{f(x)}=\sum _{n=0}^{\infty } d_nx^n$. Then the coefficients of the reciprocal of $f(x)$ can be written down. The first few terms are:
$d_0 = \frac …
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