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A functional identity involving elliptic integrals

Authors:	M. Lawrence Glasser Yajun Zhou

Affiliation:	1.Dpto.?de Física Teórica, Facultad de Ciencias,Universidad de Valladolid,Valladolid,Spain;2.Donostia International Physics Center,San Sebastián,Spain;3.Program in Applied and Computational Mathematics (PACM),Princeton University,Princeton,USA;4.Academy of Advanced Interdisciplinary Sciences (AAIS),Peking University,Beijing,People’s Republic of China

Abstract:	We show that the following double integral $$begin{aligned} int _{0}^pi mathrm {d}, xint _0^xmathrm {d}, yfrac{1}{sqrt{1-smash [b]{p}cos x}sqrt{1+smash [b]{qcos y}}} end{aligned}$$ remains invariant as one trades the parameters p and q for (p'=sqrt{1-p^2}) and (q'=sqrt{1-q^2}), respectively. This invariance property is suggested from symmetry considerations in the operating characteristics of a semiconductor Hall effect device.

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