Short Remarks on Complete Monotonicity of Some Functions
Keyword(s):
In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1 | β ( m ) ( x ) | and x m − 1 | ψ ( m ) ( x ) | are completely monotonic on ( 0 , ∞ ) for all m ∈ N , m > 2 , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function.
2020 ◽
1981 ◽
Vol 46
(2)
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pp. 452-456
2013 ◽
Vol 219
(21)
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pp. 10538-10547
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Keyword(s):
2016 ◽
Vol 111
(2)
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pp. 425-434
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