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