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Results tagged with power-series
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user 24309
2
votes
Sign of coefficients
Since the second series can be explicitely computed, you have $$\sum_{n=0}^{\infty}a_n x^n = -\frac{x}{\ln(1-x)}.$$ Now you can compute explicitely a recurrence relation giving you the exact value of …
- 5,428
6
votes
Accepted
Linearizing a power series by conjugation
You may find useful information in a recent article by D. Sauzin and al. "Explicit linearization of one-dimensional germs through tree-expansions" here, where they use "mould calculus" (introduced by …
- 5,428
10
votes
Accepted
If a formal power series over the complex numbers satisfies a polynomial identity, does it ...
The equation $\Phi(w,z)=0$ can be solved using Puiseux series. If $\frac{\partial{\Phi}}{\partial{w}}\not\equiv 0$ then there exist finitely many formal series $f(z)=\sum_{n\geq0}a_nz^{n/p}$ such t …
- 5,428