Table 2: Analytical expressions for $K_{\perp ,1}^{\rm 2D}$ , $K_{\perp ,2}^{\rm 2D}$ and $K_{\perp }^{\rm 2D}=K_{\perp ,1}^{\rm 2D}+K_{\perp ,2}^{\rm 2D}$ . $\xi (s)$ denotes the function $\xi (s) = \left [ {1 \over 4(2-s)} + {1 \over \pi (s+1)} \right ] {\sqrt {\pi }... ...mma \left ( {s+2 \over 2} \right ) \over \Gamma \left ( {s+5 \over 2} \right )}$ .
$1 \over 2$ Case $K_{\perp ,1}^{\rm 2D}$ $K_{\perp ,2}^{\rm 2D}$ $K_{\perp}^{\rm 2D}$

$1 \over 2$ $a \ll R \ll 1$ ${2 \over 3s} \left( {a \over R} \right)^2$ ${1 \over 3s} \left( {a \over R} \right)^2$ ${1 \over s} \left( {a \over R} \right)^2$

$1 \over 2$ $a \ll 1 \ll R$ ${2 \over 3s} \left( {a \over R} \right)^2$ ${1 \over 3s} \left( {a \over R} \right)^2$ ${1 \over s} \left( {a \over R} \right)^2$

$1 \over 2$ $R \ll 1 \ll a$ $(s+2) \xi (s) \left( {a \over R} \right)^2 R^s$ ${1 \over 3s} \left( {a \over R} \right)^2$ ${1 \over 3s} \left( {a \over R} \right)^2$

$1 \over 2$ $R \ll a \ll 1$ ${4 \over 3 s (2-s)} \left({a \over R} \right)^{2-s}$ ${1 \over 3s} \left( {a \over R} \right)^2$ ${1 \over 3s} \left( {a \over R} \right)^2$

$1 \over 2$ $1 \ll a \ll R$ ${\pi \over 4 s} {a \over R^2}$ ${\pi \over 4 s} {a \over R^2}$ ${\pi \over 2 s} {a \over R^2}$

$1 \over 2$ $1 \ll R \ll a$ ${1 \over 4 (s+1)} {a^2 \over R^3}$ ${1 \over 4 (s+1)} {a^2 \over R^3}$ ${1 \over 2 (s+1)} {a^2 \over R^3}$

**Table 2:** Analytical expressions for $K_{\perp ,1}^{\rm 2D}$ , $K_{\perp ,2}^{\rm 2D}$ and $K_{\perp }^{\rm 2D}=K_{\perp ,1}^{\rm 2D}+K_{\perp ,2}^{\rm 2D}$ . $\xi (s)$ denotes the function $\xi (s) = \left [ {1 \over 4(2-s)} + {1 \over \pi (s+1)} \right ] {\sqrt {\pi }... ...mma \left ( {s+2 \over 2} \right ) \over \Gamma \left ( {s+5 \over 2} \right )}$ .
$1 \over 2$ Case	$K_{\perp ,1}^{\rm 2D}$	$K_{\perp ,2}^{\rm 2D}$	$K_{\perp}^{\rm 2D}$
$1 \over 2$ $a \ll R \ll 1$	${2 \over 3s} \left( {a \over R} \right)^2$	${1 \over 3s} \left( {a \over R} \right)^2$	${1 \over s} \left( {a \over R} \right)^2$
$1 \over 2$ $a \ll 1 \ll R$	${2 \over 3s} \left( {a \over R} \right)^2$	${1 \over 3s} \left( {a \over R} \right)^2$	${1 \over s} \left( {a \over R} \right)^2$
$1 \over 2$ $R \ll 1 \ll a$	$(s+2) \xi (s) \left( {a \over R} \right)^2 R^s$	${1 \over 3s} \left( {a \over R} \right)^2$	${1 \over 3s} \left( {a \over R} \right)^2$
$1 \over 2$ $R \ll a \ll 1$	${4 \over 3 s (2-s)} \left({a \over R} \right)^{2-s}$	${1 \over 3s} \left( {a \over R} \right)^2$	${1 \over 3s} \left( {a \over R} \right)^2$
$1 \over 2$ $1 \ll a \ll R$	${\pi \over 4 s} {a \over R^2}$	${\pi \over 4 s} {a \over R^2}$	${\pi \over 2 s} {a \over R^2}$
$1 \over 2$ $1 \ll R \ll a$	${1 \over 4 (s+1)} {a^2 \over R^3}$	${1 \over 4 (s+1)} {a^2 \over R^3}$	${1 \over 2 (s+1)} {a^2 \over R^3}$

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