Positivity properties of the matrix $\left[(i+j{)}^{i+j}\right]$

Abstract

Let $p_1<p_2<\cdots <p_n$ be positive real numbers. It is shown that the matrix whose $i,j$ entry is $(p_i+p_j{)}^{p_i+p_j}$ is infinitely divisible, nonsingular and totally positive.