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Integral Equations for the Spin-Weighted Spheroidal Wave unctions |
| TIAN Gui-Hua |
| School of Science, Beijing University of Posts and elecommunications, Beijing 100876
Academy of Mathematics and Systems Science, Chinese Academy of ciences, Beijing 100080 |
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| Cite this article: |
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TIAN Gui-Hua 2005 Chin. Phys. Lett. 22 3013-3016 |
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Abstract We present new integral equations for the spin-weighted spheroidal wave fuctions which in turn should lead to global uniform estimates and should help in particular in the study of their dependence on the parameters. For the prolate spheroidal wavefunction with m=0, there exists the integral equation whose kernel is (sin x)/x, and the sinc function kernel (sin x)/x is of great mathematical significance. We also extend the similar sinc function kernel (sin x)/x to the case m≠0 and s≠0, which interestingly turn out as some kind of Hankel transformations.
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| Keywords:
04.25.Nx
04.70.-s
04.70.Bw
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Published: 01 December 2005
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| PACS: |
04.25.Nx
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(Post-Newtonian approximation; perturbation theory; related Approximations)
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04.70.-s
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(Physics of black holes)
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04.70.Bw
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(Classical black holes)
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