We present a set of formulae to extract the longitudinal deep inelastic structure function $F_L$ from the transverse structure function $F_2$ and its derivative $dF_2/dlnQ^2$ at small $x$. Our expressions are valid for any value of $\delta$, being $x^{ -\delta}$ the behavior of the parton densities at low $x$. Using $F_2$ HERA data we obtain $F_L$ in the range $10^{ -4} \leq x \leq 10^{ -2}$ at $Q^2=20$ GeV$^2$. Some other applications of the formulae are pointed out.
Categories: hep-ph