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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 1998, 3(3), 161-167; https://doi.org/10.3390/mca3030161

A Presentation Theorem of the Spherical Wave Functions

Gazi University, Faculty of Arts and Sciences, Department of Mathematics, Ankara, Turkey
Published: 1 December 1998
PDF [1456 KB, uploaded 1 April 2016]

Abstract

Let \(\phi_{i}^{*}\) and \(\psi_{i} (i=0,1,...,n-1)\) are the solutions of the equations \(\boxdot^{2} - \frac{n-1}{r^{2}}\phi_{i}=0\) and \(\boxdot^{2} \psi_{i}=0\) respectively. In this paper it is shown that if \(u\) and \(v\) are satisfied by the equations \((\boxdot^{2} - \frac{n-1}{r^{2}})^{n} u = 0\) and \(\boxdot^{2n} v =0\) respectively then \(u\) and \(v\) have the representations \(u=\phi_{0}^{*} + t\phi_{1}^{*} + ... + t^{n-1}\phi_{n-1}^{*}\) and \(v = \psi_{0} + t\psi+{1} + ... + t^{n-1}\psi_{n-1}\) where \(\boxdot^{2} = \frac{1}{r^{n-1}}\frac{\partial}{\partial r} (r^{n-1} \frac{\partial}{\partial r}) - \frac{\partial^{2}}{\partial r^{2}}\).
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Kaya, M. A Presentation Theorem of the Spherical Wave Functions. Math. Comput. Appl. 1998, 3, 161-167.

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