tanli x 

 sinh' l x ■ 



cosh" 1 .r 



tanlr 1 x 



gd.r 



TABLE 10.— MATHEMATICAL SERIES (concluded) 



1 3 , 2 B 17 T , 

 X -~3 X + T5- r -3T5- 1 +••• 



_J_^r 3 ,J_.3 £l _ I 3 5_ ^ 

 ' l 2 32 4 5 2'4'6 7 + '" 



i IJ__I3 J_ , I35^J_ 

 log _.r + 2 ^ 2 4 ^ ^ 2 4 6 6 _ r o • • • 



= log 2.t- 



11 13 1 



13 5 1 



2 2.r 2 4 4.r 4 2 4 6 6.v° 



1 - , 1 61 



= ' r - 6 - r + 24 X ~ 5040 



-v 7 +. 



-~ — sech. x 



1 sech 3 .r 1 3 sech 5 .r 



+ 



3 2 4 5 



1 5 , 61 . , 



+ -24 0+ 5O4O 0+ ' 



25 



U 2 <1) 

 (.r 2 >l) 



(.r 2 >l) 



(.r 2 <l) 



(x small) 



(x large) 



/O) = — />„ 4- />, cos — : — h /> 2 cos +. . . 



2 c c 



Cj C C 



i . 7r.r , 2irx . 



+ ai sin + a 2 cos + . . . (— c < x < c) 



6.= 7/±J/(*) 



Hfrr.r , 

 cos ax 



TABLE 11.— MATHEMATICAL CONSTANTS 



SMITHSONIAN PHYSICAL TABLES 



