The differential equation
d
2
y
/
dx
2
+ 1
dy
/
x
dx
—
y
= 0, which differs from Bessel’s Equation of zero order only in the sign of the third term ( —
y
), has two solutions denoted by I
0
(
x
) and K
0
(
x
): these solutions tend exponentially to infinity and zero respectively as
x
→ ∞ by positive values. The function K
0
(
x
) is of physical importance, particularly in connection with the electrostatic potential of a periodic linear series of charges. It has been much used recently in calculations of the electrostatic potential energy of certain crystals, for which it was found necessary to construct the following tables. It appears that the earliest tables of K
0
(
x
) are due to Aldis (‘Roy. Soc. Proc.,’ vol. 64, pp. 219-221 (1899)), who gave the values of K
0
(
x
) to 21 decimal places for values of
x
from
x
= 0 to
x
= 6·0 at intervals of 0·1, and also to between 7 and 13 significant figures from
x
= 5·0 to
x
= 12·0 at intervals of 0·1. These tables are reprinted in the ‘Treatise on Bessel Functions’ by Gray, Mathews and MacRobert (Macmillan, 1922). Jahnke and Emde, ‘Functionentafeln,’ pp. 135-6 (Leipzig, 1923), also tabulate the function K
0
(
x
)—there denoted by ½
i
πH
0
(
1
) (
ix
)—over the same range of
x
, but only to four significant figures.
Photon Emission from Solid Surfaces Irradiated with Highly Charged Ions
