52 Mr. H. G. Savidge : Tables of the 



where 



x 3 21 , 27 



77 " v/2 8n/2^ + 12«n/2^ 3 + 12^ 



c , w, 3 3 21 



s/2 -8 8v/L4- 16a' 2 ^128v2^ 3 " 



There are similar formulae throughout for the ker and kei 

 and composite functions: 



XYW_5L-.fi _i_ J_ a. 33 I 59 ! 1 



lW ~ W* Vi I 4V2. 64^ 2 + 256 V^ 3 128V f 



and similar formulae for Y^x), 'Zfa), and W x («). Zi(*) and 



W a (a?) may be found by means of the tables for Z(Vj and 

 W(#) and the formulae :— 



w ( .,)w lW =- 8 i r2 (i + i l 2 ...). 



In these 1 two series the coefficient of #~ 4 is zero. They 

 can be used when x is not less than 6 : for smaller values of 

 the argument ithese functions are tabulated 



S(#) = c sin ay 2-d cos #\/2 

 T(a?) = — d sinx^/2—c cos #\/2 



where 



75 15435 



8 V2 



~x 2 512 \/2x 4 



256' 



V2^ 6 



'-B- 



9 2475 



128^ 3 128V 



. . . . 





and these may be 



written 









S(#) — — g cos -v/r 







T(^)=— psin^, 





