The European Physical Journal C

, Volume 68, Issue 3–4, pp 683–685 | Cite as

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

  • Martin M. BlockEmail author


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 \({1\over\sqrt{v}}\).


Gluon Distribution Closed Contour Fractional Accuracy Complex Conjugate Pair Arbitrary Accuracy 
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  1. 1.
    M.M. Block, Eur. Phys. J. C 65, 1 (2010) CrossRefADSGoogle Scholar
  2. 2.
    Mathematica 7, a computing program from Wolfram Research, Inc., Champaign, IL, USA,, 2009
  3. 3.
    M.M. Block, L. Durand, P. Ha, D.W. McKay, to be published (2010). arXiv:1004.1440 [hep-ph]

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of Physics and AstronomyNorthwestern UniversityEvanstonUSA

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