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Sharp bounds for psi function
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DOI：10.1016/j.amc.2015.07.012.png)
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Abstract
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In this paper, we present the greatest value a is an element of (1/15, infinity) and the least value b is an element of (4/15, infinity) such that the double inequality L(x, a) < psi/ (x + 1) < L(x - 1, b) +1/x holds for all x > 0, where L(x, a) = 190a(2)+2 log (x(2) + x + 3a+1/3) + 45a(2)/90a(2)+2 log (x(2) + x + 15a-1/45a) and psi(x) is the classical psi function. (C) 2015 Elsevier Inc. All rights reserved.
Keywords:
Gamma function
Psi function
Monotonicity
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