Table 1: The different cases for the integrals A and B.
$1 \over 2$ Case A B

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

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

$1 \over 2$ $1 \ll au \ll uR$ ${a \over s u R^2}$ ${a \over s u R^2}$

$1 \over 2$ $1 \ll uR \ll au$ ${1 \over (s+1) \pi} {a^2 \over u R^3}$ ${1 \over (s+1) \pi} {a^2 \over u R^3}$

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

$1 \over 2$ $uR \ll 1 \ll au$ ${\pi (s+1) + 4 (2-s) \over 4 \pi (2-s) (s+1)} \left( {a \over R} \right)^2 (uR)^s$ ${1 \over s} \left( {a \over R} \right)^2$

**Table 1:** The different cases for the integrals A and B.
$1 \over 2$ Case	A	B
$1 \over 2$ $au \ll 1 \ll uR$	${1 \over s} \left( {a \over R} \right)^2$	${1 \over s} \left( {a \over R} \right)^2$
$1 \over 2$ $au \ll uR \ll 1$	${1 \over s} \left( {a \over R} \right)^2$	${1 \over s} \left( {a \over R} \right)^2$
$1 \over 2$ $1 \ll au \ll uR$	${a \over s u R^2}$	${a \over s u R^2}$
$1 \over 2$ $1 \ll uR \ll au$	${1 \over (s+1) \pi} {a^2 \over u R^3}$	${1 \over (s+1) \pi} {a^2 \over u R^3}$
$1 \over 2$ $uR \ll au \ll 1$	${2 \over s (2-s)} \left( {a \over R} \right)^{2-s}$	${1 \over s} \left( {a \over R} \right)^2$
$1 \over 2$ $uR \ll 1 \ll au$	${\pi (s+1) + 4 (2-s) \over 4 \pi (2-s) (s+1)} \left( {a \over R} \right)^2 (uR)^s$	${1 \over s} \left( {a \over R} \right)^2$

Source LaTeX | All tables | In the text