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Results tagged with divergent-series
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user 25510
3
votes
Why is it customary to have formal series at infinity in the context of resurgence and 1-sum...
The tradition probably goes back to classical results on Laplace transform: Lalace transform of a function $f$ on the positive ray is
$$Lf(\zeta)=\int_0^\infty f(z)e^{-\zeta z}dz.$$
If $f$ is of expon …
- 91.8k
4
votes
Asymptotic series
There are many modern books, for example,
MR1317343 Balser, Werner From divergent power series to analytic functions. Theory and application of multisummable power series. Lecture Notes in Mathemati …
- 91.8k
9
votes
Accepted
Riemann surface from Riccati equation
The answer to the highlighted question is "no". When $V$ is a polynomial, the
general solution of the Riccati equation is single valued, it is a meromorphic function in the complex plane. To prove the …
- 91.8k
10
votes
Accepted
What is the relationship between $\sum_{n=0}^\infty f(n) x^n$ and $-\sum_{n=1}^\infty f(-n) ...
First of all, to make sense of $f(-n)$ we need some assumptions about $f$. For example,
let
$$
\sum_{n=0}^\infty f(n)z^n \label{1}\tag{1}
$$ be a series with positive radius of convergence. Then there …
- 91.8k