An asymptotic formula for \(\pi\)
type: Item
instance of: scholarly article
title: An asymptotic formula for \(\pi\)
zbMATH Open document ID: 0665.10006
DOI: 10.1016/0022-314X(89)90072-3
author: Ferenc Mátyás
author: Péter Kiss
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \(R_ 0,R_ 1,R_ 2,..\). be a nondegenerate binary linear recurrence of integers defined by \(R_ n=AR_{n-1}+BR_{n-2}\) \((n>1)\), where \(R_ 0\), \(R_ 1=1,and\) A, B are fixed nonzero integers. It is proved that \[ \sqrt{\frac{6\cdot \log | R_ 1\cdot R_ 2\cdot \cdot \cdot R_ N|}{\log [R_ 1,R_ 2,...,R_ N]}}\quad =\quad \pi +O(\frac{1}{\log N}) \] for any sufficiently large integer N ([ ] denotes the least common multiple of numbers).
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 4087744
zbMATH Keywords: binary linear recurrence
Wikidata QID: Q106075979
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4087744