ON THE CALCULATION OF MATHEMATICAL TABLES. 63 



C^^y2-cMl ^^^^-JZ^-Y,'^' 12" ' 



2 2 



C(2r)2=a;"3>V"2„ViP|V2 



2 8 



C(4r)2=a;~3A"2;r^iP2N/2 



C(2pr)2=« SA 2nTlyp2p^^2, 



12P,=(l + 2/)2 + 4a;, 12P2=(1 +?/)«- 8a;, 

 2P,+P,='' 



'•HH' 



P,-P2=a;, Pi-P3=2/, P,-P4=^(l-^^), 



C(2j^r)^_ -^£^ P, 

 ■C(2r)2 ^' Pi' 



Then 



2uo) 2 Pu 



.i^(i-2a^)L 6.K1-.)^(1.)^- 



is a root of the equation *7=0, given by Mathews, Proc. L.M.S., 1915, 

 p. 464 ; and 



1 2 2 



2w . 4o) , 6a) 4(1-^+^^) 



