The $b$-function with respect to weights of hypergeometric ideals of codimension one

Abstract

We study the $b$-function with respect to weights of hypergeometric ideals $H_A(\beta )$, where $A$ is an $n\times (n+1)$ matrix of maximal rank. We describe the $b$-function for any weight vector $(-\omega ,\omega )$ with $\omega \in {\mathbb{R}}^{n+1}\setminus \{0\}$ and any parameter vector $\beta \in {\mathbb{C}}^n$.