A Completely Monotonic Function Involving the Divided Difference of the Psi Function and an Equivalent Inequality Involving Sums
نویسندگان
چکیده
In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established. 2000 Mathematics subject classification: primary 33B15, 26D15; secondary 26A48, 26A51.
منابع مشابه
A Class of Completely Monotonic Functions Involving Divided Differences of the Psi and Polygamma Functions and Some Applications
A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...
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