The 
ellipsoidal harmonics when 
, 
, and 
are given can be arranged in such a way that the 
th function has 
zeros between 
and 
and the remaining 
zeros between 
and 
(Whittaker and Watson 1990).
Stieltjes' Theorem
See also
Ellipsoidal Harmonic of the First Kind, Ellipsoidal Harmonic of the Second KindExplore with Wolfram|Alpha
References
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, pp. 560-562, 1990.Referenced on Wolfram|Alpha
Stieltjes' TheoremCite this as:
Weisstein, Eric W. "Stieltjes' Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StieltjesTheorem.html