ZA REPORTS ON THE STATE OF SCIENCE, ETC. 
the ‘converging factor’ is 
1 lod 1 
2a t aplat 2-8") + gape gate) 
When = is an even integer 2n, this becomes 
st vag enttany! | s 311 _ 1069 24451 4397 
4(2x)?  2(2a)8 ~— 8(2x)4 9 4 (Dx)5 — W6(Qa)@ 4(Da)7 * * 
When 2 is an odd integer 2n — 1, 
Nigar! 9 11 49 281 
at + + 
For the asymptotic series, when + = 2n + a, 
11.3.5 1.3.5.7.9 
Qe (2x)? ss (Dx)® SE pee 
the ‘ converging factor’ is 
1 
ner Ri 4 42007 _ 142323 
2a 4(2r)2?  2(2x)8 8(2ax)4 2(2x)5 16(2x)6 4(Qn)? “°° 
ata, (1-#) + oa(—gt4e—o?) + oo ( > — 17a + 622) a 
or when # = 2n + 1, & an odd integer, the series . . 
when a = 2n, x an even integer, the series . . 
The functions A(x) and B4(x) are closely related to the Confluent Hyper- 
+3.) 
geometric function M (1 
= 14204 ORY 4 Coy, Crt eee. 
The asymptotic expansion is 
Pray Abad kia al Mus eS eile GP Re / ) 
: Afra + 3 13 + 3-5 (anh * Ro i 
A table of M (1.4.2) has been constructed from these series, the latter with a 
‘ converging factor’ for large values of the argument. 
oe ee we 
ae ee ee 
x QO4(2) Q_4(x) | « Q4(x) 
[Prams per rete Sek | Pee ee eA RENE See | [Tans v Vaaeu, Soreaen 6 eee an 
0:00 | —0-636620 | +0-636620 | 0:34 | —0-474735: 
0-02 —0-628064 +0-645039: || 0:36 —0-464261 
0-04 —0-619375 -+-0-653321 : 0-38 —0-453698 : 
0-06 —0-610554 : +0-661463 0-40 —0:443051 
0-08 —0-601605 : +0-669462 0-42 —0-432321 : 
0-10 —0-592530 : +0-677316 0-44 —0-421513 
0-12 —0-583331 : + 0-685023 0:46 —0-410628 
0-14 —0-574011 : +0-692581 : 0-48 —0-399670 : 
0-16 —0-564573 +0-699988: || 0-50 —0-388643 
| 0-18 | —0-555019 +0-707242: | 0:52 | —0-377548: 
0-20 —0:545351 +0:714341: || 0-54 | —0-366390: 
0:22 —0-535573 +0-721284 0:56 | —0:355171: 
0-24 —0-525687 -+0-728067 0-58 —0-343895 : 
0-26 —0-515695 : +0-734690 || 0-60 —0-332565 
0-28 —0-505602 +0-741150 : 0-62 —0:321183 : 
0:30 —0-495409 +0:747447 0-64 —0:309753 : 
0-32 —0-485119 +0-753578 0-66 —0:298279 : 
Q_}4(z) 
+0-759541 : 
+0-765336 
-+-0-770960 : 
-++0:776413 
-+0-781692 : 
+-0-786797 
+0-791726 
+0-796478 
+0-801052 
+0-805446 : 
-+0-809660 
+0-813692 : 
+0-817542 : 
+0-821209 : 
+0-824692 
+0-827989 : 
+0-831101 : 
