On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
Hideaki Ishikawa, Yuichi Kamiya (2012)
Publications de l'Institut Mathématique
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Displaying similar documents to “Resurgence of the Euler-MacLaurin summation formula”
On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
On the convergence and summability of series with respect to block-orthonormal systems.
Nadibaidze, G. (1995)
Georgian Mathematical Journal
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Analytic and combinatoric aspects of Hurwitz polyzêtas
Jean-Yves Enjalbert, Hoang Ngoc Minh (2007)
Journal de Théorie des Nombres de Bordeaux
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In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to...
A note on differences of Power means
Slavko Simić (2009)
Publications de l'Institut Mathématique
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Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2009)
Journal de Théorie des Nombres de Bordeaux
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We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.
On a new class of refined discrete Hardy-type inequalities.
Cizmesija, A., Krulic, K., Pecaric, J.E. (2010)
Banach Journal of Mathematical Analysis [electronic only]
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A function related to the central limit theorem
Paul Bracken (1998)
Commentationes Mathematicae Universitatis Carolinae
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A number of properties of a function which originally appeared in a problem proposed by Ramanujan are presented. Several equivalent representations of the function are derived. These can be used to evaluate the function. A new derivation of an expansion in inverse powers of the argument of the function is obtained, as well as rational expressions for higher order coefficients.