Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
Journal de Théorie des Nombres de Bordeaux, Volume 21 (2009) no. 1, pp. 145-157.

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.

Nous présentons les représentations asymptotiques pour certaines sommes des réciproques des nombres de Fibonacci et des nombres de Lucas quand un paramètre tend vers une valeur critique. Comme cas limite de nos résultats, nous obtenons les formules d’Euler pour les valeurs des fonctions de zeta.

Published online:
DOI: 10.5802/jtnb.663
Carsten Elsner 1; Shun Shimomura 2; Iekata Shiokawa 2

1 Fachhochschule für die Wirtschaft University of Applied Sciences Freundallee 15 30173 Hannover, Germany
2 Department of Mathematics Keio University 3-14-1 Hiyoshi, Kohoku-ku Yokohama 223-8522 Japan
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Carsten Elsner; Shun Shimomura; Iekata Shiokawa. Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Journal de Théorie des Nombres de Bordeaux, Volume 21 (2009) no. 1, pp. 145-157. doi : 10.5802/jtnb.663. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.663/

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