Monotonicity and logarithmic convexity relating to the volume of the unit ball

摘要

Let Ω_n denote the volume of the unit ball in ?~n for n ∈ ?. In the present paper, the authors prove that the sequence Ω_n ~(1/(n ln n)) is logarithmically convex and that the sequence is strictly decreasing for n ≥ 2. In addition, some monotonic and concave properties of several functions relating to Ω_n are extended and generalized.