New bounds for the exponential function with cotangent

Abstract

In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function and a new criterion for the monotonicity of the quotient of two power series.

Notes on a Double Inequality for Ratios of any Two Neighbouring Non-zero Bernoulli Numbers

“…is strictly increasing (or strictly decreasing, respectively) if and only if 1 θ ≤ − (or 0 θ ≥ , respectively). The double inequality (2) has been cited and applied in the papers [22][23][24][25][26][27][28][29].…”