Acta mathematica scientia, Series B >
EXACT EVALUATIONS OF FINITE |TRIGONOMETRIC SUMS BY SAMPLING THEOREMS
Received date: 2007-05-22
Revised date: 2009-11-01
Online published: 2011-03-20
We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued
trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of
the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli's numbers play a role similar to that of Euler's in the old ones. Our technique differs from that of Byrne-Smith (1997) and Berndt-Yeap (2002).
Key words： Trigonometric sums; difference equations; sampling theorem
M.H. Annaby , R.M. Asharabi . EXACT EVALUATIONS OF FINITE |TRIGONOMETRIC SUMS BY SAMPLING THEOREMS[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 408 -418 . DOI: 10.1016/S0252-9602(11)60241-5
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