I am interested in understanding where in the complex plane a Heun function might vanish, or where it (or its real part) is positive. I have looked in the book of Ronveaux, as well as the NIST Handbook of mathematical functions and could not find any information on this problem. Is there anything known in that direction? I could find some information on where this happens for a hypergeometric function.

  • $\begingroup$ You should be more specific: Heun's equation includes 4 parameters, and its solutions are not "functions" in the usual sense: they are multi-valued. So you should define exactly what you mean by "Heun functions", in what region you want to define them and what do you want to know about their zeros. $\endgroup$ – Alexandre Eremenko May 15 at 0:37

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