6 problems

Borel summability conjecture. The series $h_{\mathrm{s}}(\varphi)$ might be Borel-summable in the variable $e^{-\beta\varphi}$. Since the coefficient ratio exhibits factorial growt…

Let $I_n$ denote the coefficients in Louchard's asymptotic expansion, and let $\zeta(i)$ be the ordinary Riemann zeta values. Hoffman's rational zeta-value conjecture. For each $n$…

Let $S_N$ be the approximants to a perturbative series at order $N$, and suppose that the observed behavior has $c(N)<1$ for the given terms of the series. In that case, the higher…

Let $a_n^{(l)}$ denote the perturbative expansion coefficient at loop order $l$, and let $n$ index the weak-field expansion. The leading weak-electric corrections to the imaginary…

Let $u=u^{(0)}+u^{(1)}+\ldots+u^{(N)}$ be the order-$N$ approximative standing-wave solution obtained by the iterative procedure, and let $D_b u=0$ denote the Born–Infeld equation,…

Hoffman's coefficient formula conjecture. This sequence gives every coefficient $I_n$ in terms of alternating multiple zeta values. The formula is motivated by the explicitly compu…