New upper bounds for Mathieu–type series
نویسندگان
چکیده
The Mathieu’s series S(r) was considered firstly by É.L. Mathieu in 1890; its alternating variant S̃(r) has been recently introduced by Pogány et al. [12] where various bounds have been established for S, S̃. In this note we obtain new upper bounds over S(r), S̃(r) with the help of Hardy–Hilbert double integral inequality. 2000 Mathematics Subject Classification. Primary: 26D15, 33E20.
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