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Can all the recurrence relations for spherical functions be extended to spheroidal functions



Can all the recurrence relations for spherical functions be extended to spheroidal functions



SCIENCE CHINA Physics, Mechanics & Astronomy 54(10): 1775-1782



There are two kinds of recurrence relations for the spherical functions Plm. The first are those with the same m but different l. The second are those with the same l but different m. The spheroidal functions are extensions of the spherical functions. Recurrence relations of the first kind are obtained for the spheroidal functions in recent studies. Using the shape invariance method in super-symmetric quantum mechanics, we investigate the second type of recurrence relations for the spheroidal functions. The results show that the second kind of recurrence relation can not be extended to the spheroidal functions.

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Accession: 036185577

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DOI: 10.1007/s11433-011-4469-8



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