$C_0\mathrm{,}\cdots ,C_3$

contacts of the Hall-plate

$f\left(x\mathrm{,}y\mathrm{,}z\right)$

special function expresses the trans-resistances of the Hall-plate

$r_1$

radius of the hole in the unit disk

$R_{k\mathcal{l}\mathrm{,}mn}$

trans-resistances of the Hall-plate

$R_{\text{sheet}}$

sheet resistance of the Hall-plate

$\text{vdP}$

van der Pauw function

$X\mathrm{,}Y$

coordinates in the van der Pauw plane

$X_0\mathrm{,}{Y}_0$

$X\mathrm{,}Y$ for Hall-plates without a hole

$X_1\mathrm{,}{Y}_1$

$X\mathrm{,}Y$ for Hall-plates in the limit of a very large hole

${\chi }_0\mathrm{,}{\chi }_1$

angles in the van der Pauw plane

${\varphi }_0$

electric potential at zero magnetic field

${\phi }_1\mathrm{,}\cdots ,{\phi }_3$

general azimuthal coordinates of the contacts

${\kappa }_{\xi \mathrm{,}\eta }$

Cartesian components of the conductivity tensor in the $\zeta$ -plane

$\vartheta$

exponent used in the large hole approximation

${\zeta }_0\mathrm{,}\cdots ,{\zeta }_5$

specific locations in the $\zeta$ -plane

$\star$

denotes parameters for a star-configuration of the contacts

$K\mathrm{,}E\mathrm{,}\Pi \mathrm{,}{K}^{\prime }\mathrm{,}{E}^{\prime }$

elliptic integrals and complementary ones

Z

Jacobi-zeta function

L

modular lambda elliptic function

$\text{am}\mathrm{,}\text{sn}\mathrm{,}\text{cn}\mathrm{,}\text{dn}\mathrm{,}\text{sc}$

Jacobi functions