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Stieltjes' Theorem


The m+1 ellipsoidal harmonics when kappa_1, kappa_2, and kappa_3 are given can be arranged in such a way that the rth function has r-1 zeros between -a^2 and -b^2 and the remaining m+r-1 zeros between -b^2 and -c^2 (Whittaker and Watson 1990).


See also

Ellipsoidal Harmonic of the First Kind, Ellipsoidal Harmonic of the Second Kind

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References

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, pp. 560-562, 1990.

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Stieltjes' Theorem

Cite this as:

Weisstein, Eric W. "Stieltjes' Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StieltjesTheorem.html

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