140 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



6.835 - tan- 1 



2 



6.900 



r cos x >^ t , r 2 "" 1 



7=7. (-i)"" 1 - COS (2H - I)X 



i r z 4-J v 2n i 



= I 



NUMERICAL SERIES 



*^*&$+, 



a- 



OO 



oo 



= Y- 



j k n) 



k= i 



7T 6 



c 7T b 



5 6 = - = 1.0173430620, 



S 7 ^ 



2995.286 ! 



7T 3 7T 8 



5*3 = ^ = 1.2020569032 5s = =1.1 



25.79436 - - - 9450 



7T 4 7T 9 



7T 2 

 = = 1.6449340668 



K - ri - 1-0823232337 



9 



7T 9 



= 1.0020083928, 



29749-35 



o T 6 SIQ = I.000994575I, 



55 = ^^21-5 = I '3 6 927755i s n = 1.0004941886. 

 6.901 T T 



U - =I -~n+^n-~n + =^ (-l)*' 1 T 



* J J") / ^^^^ \ * 



( 2 * + i) w> 



7T 



,.-, 



2 = 0.9159656 . . . 



w 4 = 0.98894455 .... 



UQ = 0.99868522 .... 



A table of from n = i to n = 38 to 18 decimal places is given by Glaisher, 

 Messenger of Mathematics, 42, p. 49, 1913. 



6.902 Bernoulli's Numbers. 



CO 



I. 



2. 



,_ 



I 2n 2 2n 



*= i 



( 2 2n _ 



2(2n)I 



n ~ 



+ l) 



( 2 2n-l _ l)7r 2 



k = i 



I 

 30* 



42 



30 



