Journal of Integer Sequences, Vol. 25 (2022), Article 22.6.3

Mathieu-Fibonacci Series

Živorad Tomovski
University of Ostrava
Faculty of Sciences
Department of Mathematics
30. Dubna 22
701 03 Ostrava
Czech Republic

Stefan Gerhold
TU Wien
Financial and Actuarial Mathematics
Wiedner Hauptstr. 8
1140 Vienna


Using reciprocal sums of powers of Fibonacci and Lucas numbers, we present series representations for generalized Mathieu series via Lambert-type series. An application of the Laplace-type integral for Dirichlet series yields some integral representations of reciprocal sums of the Fibonacci numbers and generalized Mathieu series. Finally, we analyze the asymptotic behavior of Mathieu-Fibonacci series by the Mellin transform method.

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(Concerned with sequences A000032 A000045.)

Received May 23 2022; revised version received June 24 2022. Published in Journal of Integer Sequences, June 24 2022.

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