MU. L. N. O. FILON ON THE KESlsTANTK TO 



, , 



( 1)" ( snih f 81111; + coslif cosi; I smh - - 

 \ (If (In I 2, 



\ , 



sm 



,0. 



TT (2m + 1) [(2m + 1)V + 16 s ] cosh 



'-'J. 



_ (cosh 2 + cos 2/3) 

 sinh ^cos , (1 - sec 2^) - 32rc^- (cosh 2f + cos 2t?) 



/ . rf d \ . , 2n+lirZ . a+,l 



(!)"( smh f sin T) -jj. + cosh f cos T; T- I sum sin ^~ 



X I -J- - ( 18 )' 





TT (27 t + 1) [(2n + 1)V - 16/3 8 ] cosh 



Q . , \ oo 2 /cosh 2 + cos 2/3 



& = re cosh f sin i, (1 - sech 2) + 32rca 2 ^ - g - -~ 



d d\ , . 2n + ltnj . 2n 



I d \ , . 2n + ltnj . 2n + 



_ ( - 1)" (^cosh f cos ; ^ - smh f sm ^ gj smh -- ^ sm - 



X 2 ^^ -^ 



7r(2 + 1) [^(271 f l) s + 16 8 ] cosh 2ra + 1?r/3 



.. . -> /cosh 2 + cos 2)8 . 



= TC cosh sm -n (1 + sec 2/8) 32nv8- - 



\cosh 2f + cos 2ij/ 



(1)* (cosh f cos -TC sinh f sin -y ) sinh 

 = v \ ' rff ? / 



sin 



X S - . (19). 



ir(2n + 1) [r 8 (2 -f- I) 2 - 16/9 8 ] cosh J~^f 



M tanh s 2,_ . 



- -Ip smh 4a a sm 4p) 



| sin 2)8 (cosh 2a + cos 2y8) (2a sech 2 2a tanh 2a) 



. 2n + lirft 

 tanh 



., 

 256<x 4 (cosh 2a + cos 2/8) 2 S 



* -f 2m 

 (a sin 4/8 sinh 4a) 

 -f ^ sinh 2a (cosh 2a + cos 20) (2/8 sec 2 2/3 tan 2/8) 





