8 problems

Clark–Ismail's coefficient-positivity conjecture. Then $\gamma(j,k)\ge0$ for all $j>1$ and $k\ge0$. This is a coefficientwise strengthening of the positivity question for $g_j$ and…

Clark–Ismail's positivity conjecture. The functions $f_j(v)$, or equivalently $g_j(v)$, are positive on $(0,\infty)$ for all $j>1$. This conjecture concerns the positivity needed t…

Let $n\in\mathbb{N}$ and define the function $x\mapsto x^n/(1-e^{-x})$ on $(0,\infty)$. Clark and Ismail's positivity conjecture. For all $x\in(0,\infty)$ and $n\in\mathbb{N}$, … T…

For $\alpha,\beta,\gamma>0$, let $F_{\alpha,\beta}^{(\gamma)}$ denote the generalized Mittag-Leffler function, and let $x>0$. Complete-monotonicity criterion conjecture. For every…

Let $F_3$ be the function defined in Theorem 3 of the source paper. A function is strictly completely monotonic on an interval if all of its derivatives have alternating signs ther…

Even-power complete-monotonicity conjecture. The function $f_{\alpha}^{[r]}$ is completely monotonic on $[0,\infty)$. In particular, $\psi_{n,c}^{[r]}$ is completely monotonic on…

Raşa's conjecture. The function $\psi_{n,c}$ is logarithmically convex. The paper proves complete monotonicity of $\psi_{n,c}$, which implies logarithmic convexity; thus this conje…

Complete monotonicity conjecture. The function $h_1$ is completely monotonic on $(0,\infty)$. This is a stronger regularity assertion about a logarithmic ratio related to the gamma…