2 problems

Let the incomplete arithmetic-geometric mean construction produce a rectangular lattice of values of $\arcsin(z)/AGM$, with lattice points obtained by choices of signs for the recu…

Let $r_n$ and $s_n$ denote the roots occurring in the AGM recursion, let $a_\infty$ and $u_\infty$ be its limiting quantities, and let $\sin_p^{-1}$ denote the principal value of t…