9 problems

Let $\sigma$ be a probability measure on $(0,\infty)$, and let $g$ be a completely monotonic function. Steutel's conjecture. Every function of the form … is an infinitely divisible…

Let $N$ particles lie on $S^{n-1}$, and let a $k$-point bound be a lower bound for their energy obtained from the corresponding moment method. Suppose there exists a completely mon…

Representing-measure conjecture. When $\mu=0$, the representing measure of $W(x)$ is…

Let $h_\lambda(x)$ and $h_\mu(x)$ be the functions defined by equation (tetra-square+poly-2), with $x\in(0,\infty)$. The completely monotonic degree of a function is the supremum o…

For $x>0$, define … A function is completely monotonic on an interval if $(-1)^n f^{(n)}(x)\ge 0$ for every nonnegative integer $n$ and every point of the interval. Qi–Guo's conjec…

Let … A function is completely monotonic if its derivatives alternate in sign on its domain. Qi–Guo's conjecture. For every integer $k\geq 1$ and every $x>0$, … Equivalently, $G'$…

Let $a_\mathrm{f}=a_\mathrm{f}(n)$ denote the critical value associated with the transition in the function $f(x,a,n)$, and let $a_\mathrm{c}$ be the critical parameter in the conj…

Let $H:(0, 0tobetabb R$ be defined by … A function $f:(0,\infty)\to\mathbb R$ is completely monotonic if it is infinitely differentiable and … Critical-parameter conjecture. There…

Logarithmic complete monotonicity conjecture. The function $\Phi_{s,t}(x)$ when $|t-s|>1$, and its reciprocal when $|t-s|<1$, are logarithmically completely monotonic on…