Addendum to: A new numerical method for obtaining gluon distribution functions G(x,Q2)=xg(x,Q2), from the proton structure function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{2}^{\gamma p}(x,Q^{2})$\end{document}

Since publication of M.M. Block in Eur. Phys. J. C 65, 1 (2010), we have discovered that the algorithm of Block (2010) does not work if g(s)→0 less rapidly than 1/s, as s→∞. Although we require that g(s)→0 as s→∞, it can approach 0 as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${1\over s^{\beta}}$\end{document}, with 0<β<1, and still be a proper Laplace transform. In this note, we derive a new numerical algorithm for just such cases, and test it for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$g(s)={\sqrt{\pi}\over \sqrt{s}}$\end{document}, the Laplace transform of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${1\over\sqrt{v}}$\end{document}.