6 problems

Let $r$ be a positive integer. The notation $[q^n]A(q)$ denotes the coefficient of $q^n$ in the series $A(q)$. Amdeberhan–Andrews–Ballantine coefficient identity. … The identity wa…

Let … Here $q$ is a complex number with $|q|<1$, so the double Lambert series defines an analytic function in its domain of convergence. Andrews–Dixit–Schultz–Yee conjecture. The f…

Identity conjecture.

Let $r$ be a positive integer, and let $[q^k]F(q)$ denote the coefficient of $q^k$ in $F(q)$. Coefficient conjecture. Then … This is a proposed coefficient relation between two Lam…

Let $a$ be a positive integer, let $n$ be a positive integer, and write $[q^k]F(q)$ for the coefficient of $q^k$ in $F(q)$. Let … be the sum of the divisors of $n$. Coefficient con…

Let $p(n)$ denote the partition function, let $\mu(n)$ denote the Möbius function, and let $s_{n,1}^{(-1)}$ denote the entries in the first column of the inverse matrix under consi…