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arXiv · 1601.00083

A proof of an open problem of Yusuke Nishizawa for a power-exponential function

Branko Malesevic·Tatjana Lutovac·Bojan Banjac
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Abstract

This paper presents a proof of the following conjecture, stated by Nishizawa in [Appl. Math. Comput. 269, (2015), 146--154.]: for $\displaystyle 0 \! \left(\frac{2}{\pi} + \frac{\pi\!-\!2}{\pi^{3}}(\pi^{2}\!-\!4x^{2})\right)^{\theta(x)}\! $ holds, where $\displaystyle \theta(x) \! = \! -\frac{(48\!-\!24\pi\!+\!\pi^{3})x^{3} }{3(\pi\!-\!2)\pi^{3}}+\frac{\pi^{3}}{24(\pi\!-\!2)}.$

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Branko Malesevic, Tatjana Lutovac, Bojan Banjac. 2016-01-01. A proof of an open problem of Yusuke Nishizawa for a power-exponential function. https://doi.org/10.7153/jmi-2018-12-35

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