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

Abstract

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 ${1\over s^{\beta}}$, 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 $g(s)={\sqrt{\pi}\over \sqrt{s}}$, the Laplace transform of ${1\over\sqrt{v}}$.