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- W4200367053 abstract "Let Kν(x) be the modified Bessel functions of the second kind. In this paper, we give the monotonicity and complete monotonicity results for several functions involving Kν(x), and establish several new sharp double inequalities for Kν(x). In particular, the double inequalities(x+a1)ν−1/2<2πxνexKν(x)<(x+b1)ν−1/2(1+a2x)ν−1/2<21−νΓ(ν)xνexKν(x)<(1+b2x)ν−1/2hold for x>0 and ν≥1 with the best constantsa1=min{c0,12ν+14} and b1=max{c0,12ν+14},a2=1max{c0,ν−1/2} and b2=1min{c0,ν−1/2},where c0=2(Γ(ν)/π)2/(2ν−1)." @default.
- W4200367053 created "2021-12-31" @default.
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- W4200367053 date "2022-04-01" @default.
- W4200367053 modified "2023-10-17" @default.
- W4200367053 title "Monotonicity and inequalities involving the modified Bessel functions of the second kind" @default.
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- W4200367053 doi "https://doi.org/10.1016/j.jmaa.2021.125889" @default.
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