Symmetries of certain double integrals related to Hall effect devices

TL;DR

This paper explores the symmetries of double elliptic integrals arising in the analysis of Hall effect devices, providing a unified mathematical framework for understanding these symmetries related to device parameters.

Contribution

It introduces a unified mathematical approach to analyze symmetric double elliptic integrals in Hall effect devices with multiple contacts, revealing underlying symmetries.

Findings

Identification of symmetries in double elliptic integrals

Unified mathematical treatment of these integrals

Application to devices with three and four contacts

Abstract

One encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz--Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical parameters of the underlying Hall effect devices. We give a unified mathematical treatment of such symmetric double integrals, in the context of Hall effect devices with three and four contacts.