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An exact expression for the leading-order (LO) gluon distribution function$G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structurefunction $F_2^{\gamma p}(x,Q^2)$ for deep inelastic $\gamma^* p$ scattering hasrecently been obtained [M. M. Block, L. Durand and D. W. McKay, Phys. Rev.D{\bf 79}, 014031, (2009)] for massless quarks, using Laplace transformationtechniques. Here, we develop a fast and accurate numerical inverse Laplacetransformation algorithm, required to invert the Laplace transforms needed toevaluate $G(x,Q^2)$, and compare it to the exact solution. We obtain accuraciesof less than 1 part in 1000 over the entire $x$ and $Q^2$ spectrum. Since noanalytic Laplace inversion is possible for next-to-leading order (NLO) andhigher orders, this numerical algorithm will enable one to obtain accurate NLO(and NNLO) gluon distributions, using only experimental measurements of$F_2^{\gamma p}(x,Q^2)$.

A new numerical method for obtaining gluon distribution functions $G(x,Q^2)=xg(x,Q^2)$, from the proton structure function $F_2^{\gamma p}(x,Q^2)$