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Approximation of the Dilogarithm Function  
 
  Authors: Mehdi Hassani,  
  Keywords: Special function, Dilogarithm function, Digamma function, Polygamma function, Polylogarithm function, Lerch zeta function.  
  Date Received: 15/04/06  
  Date Accepted: 03/01/07  
  Subject Codes:

33E20.

  
  Editors: Alexandru Lupas (1942-2007),  
 
  Abstract:

In this short note, we approximate Dilogarithm function, defined by $ $ mathrm{ dilog}(x)=$ int_1^{x}$ frac{$ log t}{1-t}dt$. Letting

$ displaystyle $ mathcal{D}(x,N)=-$ frac{1}{2}$ log^2 x-$ frac{$ pi^2}{6}+$ sum_{n=1}^N $ frac{ $ frac{1}{n^2}+$ frac{1}{n}$ log x}{x^n}, $
we show that for every $ x>1$, the inequalities
;


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