INFINITE SERIES I2Q 



6.490 





2. 



2 sinh x 



=0 



2 cosh a; 



n=o 



3. - (tanh x - i) = (- 1 )" e ~ 2nx - 



4. - 

 6.491 



By means of this formula a slowly converging series may be transformed 

 into a rapidly converging series. 



6.495 



80: 



2. COt X = - 



(2H - l) 2 7T 2 - 

 n = i 



2X 2X 2X I 



3. sec x 



n = i 

 I 2X 2X _ 2X 



X = X + ^^IT 2 ~ (27T) 2 - * 2 + ( 3 7T) 2 - 



lV - X 2 



By replacing * by c the corresponding series for the hyperbolic functions 

 may be written. 



