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  Volume 7, Issue 2, Article 46
 
A Note on a Paper of H. Alzer and S. Koumandos
    Authors: Kunyang Wang,  
    Keywords: Inequalities, Trigonometric sums.  
    Date Received: 12/07/05  
    Date Accepted: 21/01/06  
    Subject Codes:

26D05.

  
    Editors: Alexander G. Babenko,  
 
    Abstract:

In the paper `` Sharp inequalities for trigonometric sums in two variables,'' (Illinois Journal of Mathematics, Vol. 48, No.3, (2004), 887-907) Alzer and Koumandos investigated some special trigonometric sums. One of them is the sum

begin{displaymath} A_{n}^{ ast }(x,y):=sum_{k=1}^{n}{frac{cos (k-{frac{1}{2}})xsin (k-{frac{1}{2}})y}{k-{ frac{1}{2}}}}. end{displaymath}

In the present note we show that the results of [1] can be easily obtained by a very simple elementary argument. And the results we obtained are more exact.

         
       
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