This article is cited in 11 papers

On the Measure of Irrationality of the Number $\pi$

V. Kh. Salikhov

Bryansk State Technical University

Abstract: A new estimate of the measure of irrationality of the number $\pi$ is obtained. The previous result (M. Hata, 1993) is improved by means of another integral construction.

Keywords: measure of irrationality, approximation by rational fractions, partial-fraction expansion, Leibniz formula, linear form.

UDC: 511.36

Received: 25.11.2009

DOI: 10.4213/mzm8688

 English version: Mathematical Notes, 2010, 88:4, 563–573

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