In this paper, we study the representation of π as sum of arctangents. In particular, we highlight the role of linear recurrent sequences obtaining new identities. Moreover, we provide a method in order to express π as sum of arctangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality. © World Scientific Publishing Company.

Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers / Abrate, M.; Barbero, S.; Cerruti, U.; Murru, N.. - In: INTERNATIONAL JOURNAL OF NUMBER THEORY. - ISSN 1793-0421. - 10:5(2014), pp. 1309-1319. [10.1142/S1793042114500286]

Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers

Abrate M.;Barbero S.;Murru N.
2014

Abstract

In this paper, we study the representation of π as sum of arctangents. In particular, we highlight the role of linear recurrent sequences obtaining new identities. Moreover, we provide a method in order to express π as sum of arctangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality. © World Scientific Publishing Company.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2914833