On the measure of irrationality of the number π
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A new estimate of the measure of irrationality of the number π is obtained. The previous result (M. Hata, 1993) is improved by means of another integral construction.
Key wordsmeasure of irrationality approximation by rational fractions partial-fraction expansion Leibniz formula linear form
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- 3.G. V. Chudnovsky, “Hermite-Padéapproximations to exponential functions and elementary estimates of the measure of irrationality of π,” in Lecture Notes in Math., Vol. 925: The Riemann Problem, Complete Integrability, and Arithmetic Applications (Springer-Verlag, Berlin, 1982), pp. 299–322.Google Scholar
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