142 Prof. P. J. Daniell on the 



Then 



ffv*** 



- 2BC223r ^)[?^i)]+ B24 fe|-J • W) 



The author could find no tables for J 3 / 3 (A:), so that the 

 value of j 3 , h \ was found by means of an asymptotic 



O {K r ) 



expansion. 



It is known * that 



M*)—<\/— \ p " (*) sin (*- : ^i~ 7r ) + QvW cos (*- ~ip ^j/ 1 



where 



(4^-1X4^-9) (4y 2 -l)(4i; 2 -9)(4!; 2 -25)(4v 2 -49) _ 

 Pv(^)- 1 2!(8.r) 2 4! (8a?) 4 



4i/ 2 -l _ (4v 2 -l)(4v 2 -9)(4i/ 2 -25) 

 ^W- 8- . 3! (8a;) 3 " + 



Alsof Jo(*)Y (*)-J 1 (*)Y (*)= — , 



7ra; 



so that J (&r) = — vttt . 



But 



while 



T »w~ Vs { Pi ^ cos (•- 1) - <w*> sin (* - 1) } • 



hile 

 JiW =0- V 7 ^ { PiW sin(.,- 1) + Ql (.,) oos(.- 1) } 



Therefore cost x - j J = P](#)X (a?) 



™(*-j) = -Qil*)*(*)i 



where (P 1 2 +Q 1 2 )X 2 =1. 



* Schatheitlin, 'Bessel Functions,' p. 50. 

 t Schafheitlin, ' Bessel Functions, p. 47. 



