3 problems

Degree-seven Rogers–Ramanujan relation. The function satisfies

Russell's conjecture for level 2. There exists a polynomial $P(u,v)$ of degree $(p+1)/2$ in $u$ and $v$ such that

Let $R(a,b,c;q)$ denote the corresponding Ramanujan quantity, and set … where $R(q)$ is the Rogers–Ramanujan continued fraction. Also set $u=u(q)=R(1,3,10;q)$. The conjectured modu…