When adding a term to E-B approx it should lead to this for the astronomical flux. $\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)+\frac{5}{18}\frac{d^2S}{d\tau ^2}_{\tau =\frac{2}{3}}$

S is the source function, tau is the optical density, F is the astronomical flux

usually the E-B approx is just $\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)$ now we want the second term also.

I don't know how to start or get here...

  • 1
    $\begingroup$ Only someone steeped in the subject would stand any chance of understanding this question. Could you give a bit of context and explain all the symbols? $\endgroup$
    – ProfRob
    Commented Feb 12 at 6:57
  • $\begingroup$ arxiv.org/abs/1711.07026 might be helpful $\endgroup$ Commented Feb 12 at 9:01
  • $\begingroup$ And there is another completely different derivation: adsabs.harvard.edu/full/1965ZA.....61..237D (paper in German, but possibly one can follow its detailed mathematical derivation even without command of the language) $\endgroup$ Commented Feb 12 at 11:42
  • $\begingroup$ Thank you for these $\endgroup$
    – user54705
    Commented Feb 12 at 19:47
  • $\begingroup$ Looks like a Taylor expansion around a minimum at $\tau = 2/3$. $\endgroup$
    – ProfRob
    Commented Feb 13 at 14:50


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