The
spheroidal wave functions are investigated in the case $m = 1$. The integral equation is obtained for them. There are two
kinds of eigenvalues in the differential and corresponding integral equations, and
the relation between them is given explicitly. This is the great advantage of
our integral equation, which will provide useful information through the study
of the integral equation. Also an example is given for the special case, which
shows another way to study the eigenvalue problem.
References
[1]
Flammer, C. (1956) Spheroidal Wave Functions. Stanford University Press, Stanford.
[2]
Stratton, J., et al. (1956) Spheroidal Wave Functions. Wiley, New York.
[3]
Li, L., Kang, X. and Leong, M. (2002) Spheroidal Wave Functions in Electromagnetic Theory. John Wiley and Sons, Inc., New York.
[4]
Tian, G.H. and Zhong, S.Q. (2009) Arxiv: 0906.4687 V3: Investigation of the Recurrence Relations for the Spheroidal Wave Functions. Preprint.
[5]
Tian, G.H. and Zhong, S.Q. (2009) Arxiv: 0906.4685 V3: Solve Spheroidal Wave Functions by SUSY Method. Preprint.
[6]
Tian, G.H. (2010) New Method to Study the Spheroidal Functions. Chinese Physics Letter, 27, 030308. http://dx.doi.org/10.1088/0256-307X/27/3/030308
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Cooper, F., Khare, A. and. Sukhatme, U. (1995) Super-Symmetry and Quantum Mechanics. Physics Reports, 251, 267-385. http://dx.doi.org/10.1016/0370-1573(94)00080-M
[8]
Tian, G.-H. and Zhong, S.-Q. (2010) The Recurrence Relations for the Spheroidal Functions. Science China G, 54, 393-400.
[9]
Tian, G.H. and Li, Z.Y. (2011) Can All the Recurrence Relations for Spherical Functions Be Extended to Spheroidal Functions. Science China G, 54, 1775-1782. http://dx.doi.org/10.1007/s11433-011-4469-8
[10]
Tang, W.L. and Tian, G.H. (2011) Solving Ground Eigenvalue and Eigenfunction of Spheroidal Wave Equation at Low Frequency by Supersymmetric Quantum Mechanics Method. Chinese Physics B, 20, Article ID: 010304.
[11]
Tang, W.L. and Tian, G.H. (2011) Solving the Spin-Weighted Spheroidal Wave Equation with Small c by SUSYQM Method. Chinese Physics B, 20, Article ID: 050301.
[12]
Tian, G.H. (2005) The Integral Equations for the Spin-Weighted Spheroidal Functions. Chinese Physics Letter, 22, 3013-3017.
