Rit (Vísindafélag Íslendinga) - 01.06.1946, Side 28

Rit (Vísindafélag Íslendinga) - 01.06.1946, Side 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-

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