This report presents near-minimax rational approximations for the Bickley functions
K
i
1
(
x
)
K{i_1}(x)
for
x
⩾
0
,
K
i
2
(
x
)
x \geqslant 0, K{i_2}(x)
and
K
i
3
(
x
)
K{i_3}(x)
for
0
⩽
x
⩽
6
0 \leqslant x \leqslant 6
, and
K
i
8
(
x
)
K{i_8}(x)
,
K
i
9
(
x
)
K{i_9}(x)
and
K
i
10
(
x
)
K{i_{10}}(x)
for
x
⩾
6
x \geqslant 6
, with relative errors ranging down to
10
−
23
{10^{ - 23}}
. The approximations, combined with the recurrence relation, yield a stable method of computing
K
i
n
(
x
)
K{i_n}(x)
,
n
=
1
,
2
,
…
,
10
n = 1,2, \ldots ,10
, for the complete range of the argument.