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A MAGNETIC DOUBLE INTEGRAL

Part of: Discontinuous groups and automorphic forms Computational aspects Applications to specific types of physical systems Other special functions

Published online by Cambridge University Press:  18 February 2019

DAVID BROADHURST  and
WADIM ZUDILIN Open the ORCID record for WADIM ZUDILIN [Opens in a new window]
DAVID BROADHURST
Affiliation:
School of Physical Sciences, Open University, Milton Keynes MK7 6AA, UK email [email protected]
WADIM ZUDILIN*
Affiliation:
IMAPP, Radboud Universiteit, PO Box 9010, 6500 GL Nijmegen, Netherlands email [email protected] MAPS, The University of Newcastle, Callaghan, NSW 2308, Australia email [email protected]
*
✉[email protected]
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Abstract

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In a recent study of how the output voltage of a Hall plate is affected by the shape of the plate and the size of its contacts, U. Ausserlechner has come up with a remarkable double integral that can be viewed as a generalisation of the classical elliptic ‘arithmetic–geometric mean (AGM)’ integral. Here we discuss transformation properties of the integral, which were experimentally observed by Ausserlechner, as well as its analytical and arithmetic features including connections with modular forms.

Keywords

elliptic integralarithmetic–geometric meanmodular formarithmetic differential equation

MSC classification

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 33C20: Generalized hypergeometric series, $_pF_q$ 33E05: Elliptic functions and integrals 33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.) 82D40: Magnetic materials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 1 , August 2019 , pp. 9 - 25
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

References

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