TY - JOUR
AU1 - Glasser, M.
AU2 - Zhou, Yajun
AB - We show that the following double integral 
$$\begin{aligned} \int _{0}^\pi \mathrm {d}\, x\int _0^x\mathrm {d}\, y\frac{1}{\sqrt{1-\smash [b]{p}\cos x}\sqrt{1+\smash [b]{q\cos y}}} \end{aligned}$$








∫

0

π

d

x

∫
0
x

d

y

1



1
-

p

cos
x




1
+

q
cos
y












remains invariant as one trades the parameters p and q for 
$$p'=\sqrt{1-p^2}$$




p
′

=


1
-

p
2






 and 
$$q'=\sqrt{1-q^2}$$




q
′

=


1
-

q
2






, respectively. This invariance property is suggested from symmetry considerations in the operating characteristics of a semiconductor Hall effect device.
TI - A functional identity involving elliptic integrals
JF - The Ramanujan Journal
DO - 10.1007/s11139-017-9915-4
DA - 2017-06-26
UR - https://www.deepdyve.com/lp/springer-journals/a-functional-identity-involving-elliptic-integrals-2po3tbjBsW
SP - 243
EP - 251
VL - 47
IS - 2
DP - DeepDyve
ER -