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For an attractive Coulomb potential $V(r)=-\kappa /r$ with $\kappa >0$, let $m$ be the relative-motion mass, using the reduced mass for a two-body system. A bound energy $E<0$ definesIn the orbital angular momentum sector $\ell$, the Radial Schrodinger equation isExtract the regular origin power and decaying exponential by $R=r^{\ell }{e}^{-\gamma r}S(r)$, with $S={\sum }_{k\ge 0}{a}_k{r}^k$. Equating powers gives the recurrence relationThe regular confluent hypergeometric function otherwise contains an exponentially growing large-radius part. A physical bound state therefore requires termination: if $S$ has degree $q\ge 0$, then $a_{q+1}=0$, soHere $N$ is the principal quantum number and $q$ counts positive radial nodes. For $\ell =0$, the recurrence reduces to $a_k=(2\gamma k-\beta )a_{k-1}/[k(k+1)]$; that denominator is an s-wave specialization, not the general angular-momentum recurrence. Regularity at the origin and normalizability at infinity are both essential boundary conditions.