Goodwin–Staton integral

In mathematics the Goodwin–Staton integral is defined as :[1]

It satisfies the following third-order nonlinear differential equation

Properties

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Symmetry:

 

Expansion for small z:

 

References

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  1. ^ Frank William John Olver (ed.), N. M. Temme (Chapter contr.), NIST Handbook of Mathematical Functions, Chapter 7, p160,Cambridge University Press 2010
  • http://journals.cambridge.org/article_S0013091504001087
  • Mamedov, B.A. (2007). "Evaluation of the generalized Goodwin–Staton integral using binomial expansion theorem". Journal of Quantitative Spectroscopy and Radiative Transfer. 105: 8–11. doi:10.1016/j.jqsrt.2006.09.018.
  • http://dlmf.nist.gov/7.2
  • https://web.archive.org/web/20150225035306/http://discovery.dundee.ac.uk/portal/en/research/the-generalized-goodwinstaton-integral(3db9f429-7d7f-488c-a1d7-c8efffd01158).html
  • https://web.archive.org/web/20150225105452/http://discovery.dundee.ac.uk/portal/en/research/the-generalized-goodwinstaton-integral(3db9f429-7d7f-488c-a1d7-c8efffd01158)/export.html
  • http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_02.pdf
  • F. W. J. Olver, Werner Rheinbolt, Academic Press, 2014, Mathematics,Asymptotics and Special Functions, 588 pages, ISBN 9781483267449 gbook