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M. Cihat Dagli

Publications and source records attributed to M. Cihat Dagli.

2 recordsLinked to original sources
arXiv2016

Character analogue of the Boole summation formula with applications

In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet $L-$function and its derivative is evaluated at $s=0$. Some applications of the character analogue of the Boole summation formula and the integral representation are given about the alternating Dirichlet $L-$function. Moreover, the reciprocity formulas for two new arithmetic sums, arising from utilizing the summation formulas, and for Hardy--Berndt sum $S_{p}\left( b,c:χ\right) $ are proved.

math.NT↗
arXiv2016

On the integral of products of higher-order Bernoulli and Euler polynomials

In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish the connection between the results and the generalized Dedekind sums and Hardy--Berndt sums. Finally, the Laplace transform of Euler polynomials is given.

math.NT↗