ON THE CALCULATION OF MATHEMATICAL TABLES. 83 
The Neumann G Functions. 
The Neumann Functions G,(x) of order greater than unity are of 
frequent occurrence in physical problems, such as the diffraction of light, 
pressure of radiation, &c. Tables of the functions have been found from 
those of G,(x) and G,(x) by (a) direct calculation and (b) logarithmic 
computation from the recurrence formula 
Grnsi(X) a s G,,(z) i 
and verified in the case when z is an integer by the relation 
Jn(%) Gpii(z) — Inas(2) G,(2) = 
G,-1(2) 
The Bessel Functions J,,(x) for positive integral values of n and w have 
been given by Meissel for 7 = 1 tox = 24 
The Tables may be used to calculate G,(x) for other values of: the 
argument x by employing the following formula : 
G(e +h) = G,(x) +h E Cota) (2) 
a al {a — 1) 
gy? 
- 1) @(@ + = Gn) shh 
2! 
Tables of the Newmann Functions. G,(«). 
x= O1 0°2 03 0°4 0°5 
+ 2-40998 +1-69820 -+1-26806 | +0-95194 -+-0-69825 
+10:14570 -+5:22105 +3-60200 +2-79739 +2-31138 
— _— — — +8:54729 
Gi(z) | a= 06 07 0'8 09 1:0 
n=0 +0-48461 +0-29950 +0-13635 —0-00884 —0-13863 
1 -+1-97982 +1-73298 + 1:53647 --1:37150 -+1-22713 
2 +6-11479 +4-65188 +3:70481 | +3-05663 -+2-59289 
| 3 — — _— | — +9-14442 
Gi(e) |a2= 11 1:2 1:3 14 15 
n=0 —0-25473 —0-35827 | —0-45009 —0-53076 —0-60075 
1 -+-1-09660 +0-97568 +0-86161 -+0-75264 -+0-64765 
2 +2-24855 +1-98440 +1-77565 -+-1:60597 +1-46429 
is +17-07994 + 5-63900 +4-60192 +3-83584 +3-25711 
G(x) T= gA:6 17 18 1:9 2:0 
n= 0 —0-66041 —0-71004 —0:74995 —0-78040 —0-80170 
1 +0-54597 +0:44725 +0:35133 +0-25825 +0-16813 
2 -- 1-34287 + 1-23622 +1-14032 +1-05224 +0-96982 
3 -+2-81121 +2-46149 +2-18271 +1-95700 +1-77152 
4 +9-19916 +7-45141 +6:13537 +5-12776 +4-34473 
QZ 
