ON THE CALCULATION OP MATHEMATICAL TABLES. 113 



M-)=i'^-log^)Xb{.) + fl^^ + f^^jy-^+ . . .., where 



c,=':o.=!^c.=?^4 <^'=lX(j)+lX{2V^i) 



5 _43 _257 



=4 '^-24 '^"120 • ■ 



j=i 



Vr(.) = («-log.)V%) + 4eA)H|I,^+^^/^]5+ • • . . 

 The coefficients are Ci—^, c-i—-., ^^~a' • • • • 

 Zr(x)^(a-los X) Zb(x)- 1 +(V2)%5 {V.y .247 (V.)^^ , 



The coefficients are Ci—^ ; Cj — g; "3— -^^ ; 



The coefficients are c,— ; c, — - ; Cq — — ; 



' 4 ^ 8 ^ 12 



+ C3 (•V.)"+ 



^|3|3|6 



2V22ll (2. 6)2|3 (2.6.10)^(5^ • • • y -r i|i|i|2^ 'l2|214 



■^''^,3^76+ 



where .,=2; «,=67; .3=^^^ n,=^7659 ^ _ ^ 

 '■ ' - 18' ^ 3600 ^ 88200 



, 8r-8 3(4r-l) 



' '"' 2r(2r-l) ' 8r2(2r— 1) 



Yk{x)= { (.-log xOH^g } Vfe(x) + 2(a-loga;) [ ie/.)^ + |4|^3 + -.- } 



3 ' (2. 6)2i5 ' ' ' ' J^8 \l\i ' 288 11 |2 jS' 



4\ ^2'%'^(2.6y<y ' ' ' ;+8 iiir 



1916 



