72 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



3.310 The values of five hyperbolic functions in terms of the sixth are given in 

 the following table : 



3.311 Periodicity of the Hyperbolic Functions. 



The functions sinh x, cosh x, sech x, csch x have an imaginary period 27ri, e.g. : 



cosh # = cosh (x + 27rin), 

 where w is any integer. The functions tanh x, coth x have an imaginary period iri. 



TT "2 7T7 



The values of the hyperbolic functions for the argument o, i, iri, - > 

 are given in the following table : 



