Abstract
We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We claim that, when parameters $\delta$ of the integrand are non-resonant, the $\mathcal{D}$-module corresponding to Euler-Laplace integral is naturally isomorphic to GKZ hypergeometric system $M_{A}(\delta)$ where $A$ is a generalization of Cayley configuration. As a topological counterpart of this isomorphism, we establish an isomorphism between certain rapid decay homology group and holomorphic solutions of $M_{A}(\delta)$.
Citation
Saiei-Jaeyeong Matsubara-Heo. "Euler and Laplace integral representations of GKZ hypergeometric functions I." Proc. Japan Acad. Ser. A Math. Sci. 96 (9) 75 - 78, November 2020. https://doi.org/10.3792/pjaa.96.014
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