tests.tex

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\title{Find the differential equation}
\author{Veronica Fantini}

\begin{document}

\maketitle
For $n\geq 3$, the thimble integral $K_n(z)$ is defined as follows 
\begin{equation}\label{int_higher-Ariy}
K_n(z) =  \int_{\Lambda} \exp\left[-z\big((n-1)^{n-1} u^n - nu\big)\right]\,du
\end{equation}

Our goal is to find the ODE that has \eqref{int_higher-Ariy} as a solution. 

For $n=3$, the solution is given by the modified Bessel equation with parameter $1/3$. 

==================================================

For $p\geq 1$, consider the thimble integral 
\[I_+(z,p):=\frac{1}{2\pi i}\int_{\Gamma_1} e^{-z(4u^3-3u)} \frac{du}{u^p}\]

\end{document}