Statistical mechanics 



Subtracting this value from (184) we get 



, , 1 _ I e dz 



0 



— z 



1 / e dz 



x'^ J 1 -|- /^/x'^ x^ ' 



0 



where 



00 



/.•3 <l .?^e~^ = 2. 



0 



It follows that <!^{x) differs from 1/x by a quantity numerically smaller than 

 which for large x may be made as small as we please. 

 Furthermore we have: 



1 _ ^ s'^x^ 



1 + e^x' 1 + e^x'^ 



and 



where ^5<;|^. In like manner we may proceed to the higher (negative) powers 

 of x. It evidently follows that this divergent series may be used for numerical 

 work as soon as x has a large value. The error in the evaluation is always 

 numerically smaller than tlie next non-considered term in the series. 



A table of the functions <\j[x), ^^x) and T is given at the end of this memoir 



From (185*) we deduce: 



1 \^ |ö 1 7 



i// [A/ 'Aj lA/ 



