ber and bei and ker and kei Functions. 51 



and equating the real and imaginary parts we obtain 



ber,r = -^JL ( / V2 + s/t cos— + \/2 - V2 sin ^] r 

 + (\/2+>/2sin-^= -v/2->/2cos-^^ j , 



beia? = **, ((\/2+^2sin-^-^2-^cos-4-V- 



2^2^ IV ^2 V^2/ 



-('\/2+^cos-^+v/2--v / 2sin^ 5 | r 



where 



l 2 l 2 . 3 2 . 5 2 l 2 . 3 2 . 5 2 . 7 2 l 2 . 3 2 . 5 2 . 7 2 . 9 2 



7 '~ + 8>/2a [3(8#)V2 J4(8^) 4 !5(8,.)V2 + 



1 2 _ 1 2 .3 2 1 2 .3 2 .5 2 1 2 .3 2 .5 2 .7 2 .9 2 



8n/2^ |2(8.r) 2 |3(8^) 3v/ 2 |5(8^) b ^2 



These expressions reduce to 



bera?=/cos^=— <j>\ 



beU-=/sin(-^-</>j, 



where 



_fi^ f 1 1 133 _ 27690 -) 



7 v/2^?l 8/2/^ 2 2048 V2# 3 512 V-/ 



Hn^-^ 1 . v/ ^" 1 i 12 - 5 ^ , 20v/2-13 , 435y/2"-560 

 tan</>_ ^2-1 + —^- + 64 ^ + 256g8 + - m2 ^ ... 



From the above we obtain the following formula? : 



YM- ^ J~1 -t -i- _i 33 3594 > 



W ~2^l V2.f 64a 3 256 V^ 3 128V" j" 



,Wi f 3_ _9_ 75 4950 l 



V W = 27r7 r L 4V 2* <34# 2 + 256 •I* 3 128V ' ' ' J 



Z(.*) 



JJ_ 3 lo 45 630 | 



Vx Is/ 2 ** 64\/2^ 512^ 3 12S 2 V / 2x i ") 

 w *_£^ TJ_ ^ 9 39 150 ^ 



W " 2™ lv/2 + 8.. + 64 V 2.*- 2 + 512 t u 3 + 12S 2 n/2^ " / 



ber' x— ,- — cos oj, 



V27T07 



bei' # = ,- — sin &>, 





