ON CALCULATION OF MATHEMATICAL TABLES. 287 
Lommel-Weber Q. Functions of Zero and Unit Orders—contd. 
z | Oe) | Oe) |e | Dole) A@) | 
'15-80 +0-169610: | +0-160016: | 15-90 4.0-153040: +0-171096 : 
+82 -+0-166386: | -+0-162367 || . -92 +0:-149598 : -+-0-173106 : 
+84 +0:163116 | +0-164651: || -94 +0:146117 -+-0-175045 : 
-86 ---0:159801 +0:166868 || -96 +0:142597 +0-176914 
-88 -+.0-156442 | -+0-169017 | -98 -+0-139041 +0:178710 : 
| 16-00 +0-135449: | -+0-180434: 
Bessel-Clifford Functions of Zero and Unit Orders. 
The function C,(x) is defined by the series 
a 2 x x” 
co 
De Meret UN (27/2) =1—z4 gra 31a a oe 
The successive derivatives of C,(x) give the series which represent the 
functions of higher integral order in accordance with the definition 
C,(2) = (—yn ne) = (—x)/TL(n-+ k)EL(h), 
k=0 
eis TIRED Oar a a? x 
Prateek ROME TTT aT ee 
Commencing with the two hundred values of x from 0-1 to 20-0, z=2./a2 was 
obtained in each case to nine significant figures, from tables of square roots and the 
corresponding values of J,(z) calculated from Meissel’s well-known table: C,(zx), 
the first derivative of C,(x), was found from central differences by the relation 
d-f(a) _ a ae Nir 
1] fr @—h F(t gh Fela). | 
The more vant properties and the applications of the Bessel-Clifford functions 
are set out in detail by Sir George Greenhill in the Phil. Mag., Nov. 1919. 
x C(x) C, (x) x Co(x) C,(z) 
0-00 +1-:000000 | -+1:000000 | 0-50 +0-559134 -+0-769986 : 
-02 +0-980100 +0:990033: || -52 +0-543818 : +0-761582 
“04 +0-960398 | +0-980133 | -54 -+0:528670 : +0-753235 : 
-06 +0-940894 | +0-970298: -56 +0:513689 +0-744947 ; 
08 +0-921586 +0-960530 58 +0-498872 +0-736717 
0-10 +0-902472 : --0-950826 : 0-60 +0-484219 : +0-728544 
12 +0°883552 : +0:-941188 -62 +0-469730 +0-720428 : 
14 +0-864824 : +0-931614 : 64 +0-455402 +0:-712370 
16 +0:846287 : +0-922105 -66 +0:441235 +0-704368 
“18 +0-827940 +0-912660 -68 +0:427227 +0-696422 : 
0:20 +0-809780 : + 0-903278 : 0-70 +0-413377 : -+0-688533 
+22 +0-791808 +-0-893960 72 +0-399685 : +0-680699 
-24 +0:774021 : +0-884705 ‘74 +0-386149 : +0-672921 
+26 +0-756419 : -+0-875513 -76 +0-372768 +0-665198 
+28 +0-739001 +0-866383 ‘78 +0:359541 +0-657529 : 
0-30 +0-721764 +0-857315 : 0-80 +0-346466 : +0-649916 
+32 +0:704708 +0-848309 : *82 +0:333544 +0-642357 
+34 +0-687831 +0-839365 “84 -+-0:320772 + 0-634852 
+36 +0-671132 : +0°830482 86 +0:308149 : -+-0-627401 
‘| -38 +0-654611 : +0-821659 : -88 + 0:295675 : +0-620003 
| 0-40 +0-638266 -+-0-812897 : 0:90 +0:283349 +0:612658 : 
| -42 +0-622095 +0-804196 92 +0-271169 +0-605367 
44 +0-606098 +0:795554 : +94 +0-259134 +0-598128 
+46 +0-590272 : +0:786972 : -96 +0:-247243: +0-590941 : 
48 4+-0-574618 : 4-0°778450 || -98 -+-0-235496 +0-583807 : 
