From Madhava-Leibniz to Lehmer’s limit. (English) Zbl 1503.40003
The authors offer a new insight into a family of infinite series originally studied by D. H. Lehmer [Am. Math. Mon. 92, 449–457 (1985; Zbl 0645.05008)] and further studied by F. J. Dyson et al. [Am. Math. Mon. 120, No. 2, 116–130 (2013; Zbl 1310.11122)]. Here the authors show that phenomena discussed by Lehmer derive from simple transformations of the well-known Madhava-Leibniz series for \(\frac{\pi}{4}\).
Reviewer: Leila Miller-Van Wieren (Sarajevo)
MSC:
| 40A25 | Approximation to limiting values (summation of series, etc.) |
| 40A30 | Convergence and divergence of series and sequences of functions |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
Software:
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