ON THE FURTHER TABULATION OF BESSEL, ETC., FUNCTIONS. 47 
; (69) AG a al @—6_o—r 2—k 
aes Wee 
28 
JK _vT 
a@—d o—s’ as a-s (@—d VE’ (k—-ifP VE 
if K, Tf is the value of X, §, for s = k, s =r. 
The homogeneity factor 
M=3V[(4 — y) G—9)] 
r7—g VB’ 
will make 
Mdz _ V(s, — 83)ds 
(7) Mex, ro 4: aa 
and then 
(v2 —h)da _ (w@—¢ +5 —h)dz 
a) VX /X : 
in which 
vad a ds | 
e J Vx a—s S/§’ 
(74) ES % & is made to depend on | Te a4 
because, conversely 
(75) VT ds __'—-k VT V2 ds 
t—s VS a2—k VB os VS 
_a-k VK (#—?)do 
Sea pal CME SAAS a 
= 1 ee et 
é—-hk aw—k} SX” 
The integrals in (65) can thus be made to depend on a numerical 
value entered in the Table, of which four specimen pages are given 
here, calculated for the modular angle 
6 = 15°, 45°, 75°, and 80° ‘1, when K = 2K’. 
It, will serve no useful purpose to. go much below 0=15°, as the 
functions are then indistinguishable from 
OK’ fs 
== 1-3 NA ma Zo 
C(r) = 14+ an7,7 2(90:— r) 
A) = sim 2 B (r) = cos r° 
E (r) = F(r) = 3 (1 — «’) sin Qr°. 
