Geodesic
On the Measure of Irrationality of the Number~$\pi$
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 583-593

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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. 
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     author = {V. Kh. Salikhov},
     title = {On the {Measure} of {Irrationality} of the {Number~}$\pi$},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a9/}
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V. Kh. Salikhov. On the Measure of Irrationality of the Number~$\pi$. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 583-593. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a9/