All Questions

I'm searching for some references about groups of invariance of the Painlevé property other than the book of Robert Conte or more generally birational transformation of Riemann surfaces.

Looking for references for the following theorem. Given the formal Taylor series/exponential generating function $$T(z) = \sum_{n \ge 1} a_n \; \frac{z^n}{n!},$$ for which the indeterminates $a_n$ and ...

Is the following theorem known, or can be easily derived from known results? Consider the differential equation $$w''-kz^{-1}w'=(\lambda+\phi(z))w,$$ where $k>0$ is fixed, $\lambda$ is a large (...

I'm looking for a gentle an concise introduction to complex-variable differential equations. Eventually, I need to look at complex PDEs, but I assume one starts with complex ODEs. Mostly, I'm just ...

Has the system of ODEs $$\frac{dx}{dt}=P(x,y)\\ \frac{dy}{dt}=Q(x,y) $$ been studied for the special case of the polynomials $P$ and $Q$ being a harmonic pair, i.e. the real and imaginary part of ...

Suppose I have an annulus $U\subset \mathbb{C}$ and a single-valued holomorphic function $V:U\to \mathbb{C}$. I would like to know if there are (tractable) conditions on $V$ that ensure that the ...