Abstract
The lowest zeros of the cross-products of derivatives of spherical Bessel functions are not obtainable from a McMahon-type formula. This paper derives an analytical approximation for these lowest, “exceptional”, zeros, through to 4th order in a parameter specifying the thinness of the corresponding concentric spherical region.
Zusammenfassung
Die kleinsten Nullstellen der Kreuzprodukte der Ableitungen von spherischen Bessel-funktionen können nicht durch eine Formel von McMahon Typ erhalten werden. Durch eine Entwicklung bis zu vierter Ordnung in einem Parameter proportional zur Dicke des zugeordneten spherischen Gebietes berechnen wir eine analytische Näherung für diese kleinsten, „außergewöhnlichen“, Nullstellen.
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Gottlieb, H.P.W. On the exceptional zeros of cross-products of derivatives of spherical Bessel functions. Z. angew. Math. Phys. 36, 491–494 (1985). https://doi.org/10.1007/BF00944640
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DOI: https://doi.org/10.1007/BF00944640