On the monotonicity and convexity of the
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Cristinel Mortici
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Article
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2011
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Elsevier Science
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English
โ 193 KB
proved that the function ฮธ (x) defined by ฮ (x + 1) = โ 2ฯ (x/e) x e ฮธ (x)/12x is strictly increasing for x โฅ 1. The aim of our work is to prove that -x -1 ฮธ โฒโฒโฒ (x) is strictly completely monotonic on (0, โ) . As direct consequences, we show that ฮธ is strictly convex on (0, โ) , and then we prove t