Some Families of Apéry-Like Fibonacci and Lucas Series

Robert Frontczak, Hari Mohan Srivastava and Živorad Tomovski
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Robert Frontczak: Landesbank Baden-Württemberg (LBBW), D-70173 Stuttgart, Germany
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Živorad Tomovski: Department of Mathematics, Faculty of Science, University of Ostrava, 70103 Ostrava, Czech Republic

Mathematics, 2021, vol. 9, issue 14, 1-10

Abstract: In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed out.

Keywords: Riemann Zeta function; central binomial coefficient; Catalan numbers; Fibonacci numbers; Lucas numbers; harmonic numbers; Lerch’s transcendent (or the Hurwitz–Lerch zeta function) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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