Monotonic series for fractions near π and their convergents.

Autor: Lucas, Stephen K., Nimbran, Amrik Singh
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Zdroj: Mathematical Gazette; Jul2022, Vol. 106 Issue 566, p300-309, 10p
Abstrakt: We describe various methods to derive monotonic infinite series for fractions near π and obtain a variety of series for the special case of its convergents. These series immediately show that π is clearly different from these fractions, replicating with series the results in Dalzell [1, 2] and Lucas that used integrals with non-negative integrands to represent the gaps between π and fractions. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index