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

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Abstract

There are two kinds of recurrence relations for the spherical functions P m l . 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 supersymmetric 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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References

  1. Flammer C. Spheroidal Wave Functions. Stanford: Standford University Press, 1956. Chapters 1–3

    Google Scholar 

  2. Stratton J. Spheroidal Wave Functions. New York: Wiley, 1956. Chapter 1

    MATH  Google Scholar 

  3. Li L W, Kang X K, Leong M S. Spheroidal Wave Functions in Electromagnetic Theory. New York: John Wiley and Sons Inc., 2002. Chapters 1–3

    Google Scholar 

  4. Infeld L, Hull T E. The factorization method. Rev Mod Phys, 1951, 23: 21–68

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Tian G H, Zhong S Q. Investigation of the recurrence relations for the spheroidal wave functions. arXiv, 2009, 0906.5563v3

  6. Tian G H, Zhong S Q. Study the spheroidal wave functions by SUSY method. Arxiv, 2009, 0906.4685v3

  7. Tian G H, Zhong S Q. Ground state eigenfunction of spheroidal wave functions. Chin Phys Lett, 2010, 27: 040305

    Article  ADS  Google Scholar 

  8. Tang WL, Tian G H. Solve the spheroidal wave equation with small c by SUSYQM method. Chin Phys B, 2011, 20: 010304

    Article  ADS  MathSciNet  Google Scholar 

  9. Tian G H. A new method to solve the spheroidal wave equations. Chin Phys Lett, 2010, 27: 030308

    Article  ADS  Google Scholar 

  10. Tian G H, Zhong S Q. The recurrence relations for the spheroidal functions. Sci China Phys Mech Astron, 2011, 54: 393–400

    Article  ADS  Google Scholar 

  11. Cooper F, Khare A, Sukhatme U. Supersymmetry and quantum mechanics. Phys Rep, 1995, 251: 267–385, and references therein

    Article  MathSciNet  ADS  Google Scholar 

  12. Gradsbteyn I S, Ryzbik L M. Table of Integrals, Series, and Products. 6th ed. Singapore: Elsevier pte. Ltd, 2000. 110

    Google Scholar 

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    GuiHua Tian & ZhaoYang Li

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  1. GuiHua Tian
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  2. ZhaoYang Li
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Correspondence to GuiHua Tian.

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Tian, G., Li, Z. Can all the recurrence relations for spherical functions be extended to spheroidal functions. Sci. China Phys. Mech. Astron. 54, 1775 (2011). https://doi.org/10.1007/s11433-011-4469-8

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  • DOI: https://doi.org/10.1007/s11433-011-4469-8

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