Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 28

28
formulas, but, as a rule, necessitates more cumbersome
transformations if r, is great. By using /'^=5, s = 6 and
t= \.\A, I obtain from (18) the equations
du
0.78146 ij — 0.49053 = 0.69682 + RSfi (y)
0.89012 y + 0.75927
du
' = — 0.98776 + /?,
dt ^ 5
du
whence u = 0,04326, —— = — 1.3516
dt
and for y = 0, 7=1.14 + 0.032 = 1.172.
4. BESSEL’S DIFFERENTIAL EQUATION.
From Bessel’s differential equation
, d2y dy , ,
x1---2 + x - + (x2 — m) y = 0 (49)
dx dx
using asymptotic differentiation (23), I get
U =
(k — n) (k + n)
n = 0
n ,n
x d y0
n\ dxn
,2 2 , 2
/r — m + x
(50)
Between the derivatives at the origin (x = 0), the following
relation exists
/2 2, d lh / ., ^ Uo
(m n) -— — n (n - 1) —— 2
ax ax
(51)
and obvious difficulties present themselves in using (50)
if m is an integer. On the other hand the denomina-