Journal
JOURNAL OF INEQUALITIES AND APPLICATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/s13660-015-0724-2
Keywords
gamma function; psi function; monotonicity
Categories
Funding
- Natural Science Foundation of China [11301127, 61374086, 11171307]
- Natural Science Foundation of Zhejiang Province [LY13A010004]
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In this paper, we present the best possible parameter a is an element of (1/5, infinity) such that the functions psi' (x + 1) - L-x(x,a) and psi ''(x + 1) - L-xx(x,a) are strictly increasing or decreasing with respect to x is an element of(0,infinity), where L(x,a) = 1/90a(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. As applications, we get several new sharp bounds for the psi function and its derivatives.
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