128 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



6.480 



i. sinh- 1 x = x - x* + -^- x 5 - . . . 

 2-3 2-4-5 



=o 



2.' sinh" 1 # = log 2# H --- - -- 7 + 

 2 2# 2 2-4 4# 4 



, , , III-3I 



3. COSH" 1 X = log 2# --- r * 7 ... 



2 2o: 2 2-4 4# 4 



log 2X - / . 9 . ' - X~ 2n 

 2n2 



, , 1,1,1 



4. tanh -1 x = x + -x* + -x 5 + - 



3 5 7 



. , , i i ii 1-3 i 



5. sinn" 1 - = + ~ - 



x x 2 3# 3 2-4 5# 5 



2 , ,. 



2 2n (w!) 



, , I , 2 IX 2 I T, X 4 



6. cosh- 1 - = log - * ... 



X X 22 2-4 4 



= seen" 1 x = log 



I 2 I X I ' T> X 



7. sinh" 1 - = log - H * 



x x 22 2-4 4 



8. 



x x $x* $x 



= coth" 1 x = 



2U + I 



