engleski

Quotient mean series

The well-known Mathieu series can be transformed into the form containing the Geometric and Quadratic mean. This connection leads us to the idea to introduce and research the so-called Quotient mean series as a generalizations of Mathieu's and Mathieu-type series. We give an integral representation of such series and their alternating variant, together with associated inequalities. Also, special cases of quotient mean series, involving Bessel function of the first kind, have been studied in detail.

Quotient mean series; Dirichlet--series; Mathieu series; Means; Gamma function; Euler--Maclaurin summation formula; Bessel function of the first kind; Landau estimates; Olenko estimates

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