I want to solve the following equation. Unfortunately solve doesn't do the job. Is there any other way or am I doing something wrong?

Solve[Sum[Binomial[8, d]*1/2*(1 + Erf[(-d + 0.5*(l + k))/(0.215*(l - k)*Sqrt[2])])
, {d, 0, 8}] == n, {k, l, n}]

$k, l, n$ are real numbers.

$n$ should be positive and

$k$ should be smaller than $l$.

I am relatively new to Mathematica and I am sorry if this problem is to trivial for you.

  • $\begingroup$ How would you expect to solve a function with errorfunctions in it analytically? $\endgroup$
    – Feyre
    Commented Oct 29, 2016 at 11:37
  • $\begingroup$ Welcome to Mathematica.SE! 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour and check the faqs! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$
    – user9660
    Commented Oct 29, 2016 at 12:08
  • $\begingroup$ I don't need an analytically correct answer. An approximation would be sufficient. But also NSolve and Reduce won't work $\endgroup$ Commented Oct 29, 2016 at 13:03
  • $\begingroup$ Well, There's only one equation and 3 unknown, so NSolve[] doesn't have enough to work on. $\endgroup$
    – Feyre
    Commented Oct 29, 2016 at 13:08
  • $\begingroup$ But it also doesn't work if I specify two variables... $\endgroup$ Commented Oct 29, 2016 at 13:15

1 Answer 1


How about

FindInstance[Sum[Binomial[8, d]*1/2*(1 + Erf[(-d + 0.5*(l + k))/(0.215*(l - k)*Sqrt[2])]),{d, 0, 8}] == n && k < l && n > 0, {k, l, n}, Reals]

{{k -> -0.24711, l -> 1, n -> 1}}?


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