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On the Addition Theorem for Jacobi Polynomials

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Coincidence Studies of Electron and Photon Impact Ionization

Part of the book series: Physics of Atoms and Molecules ((PAMO))

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Abstract

Jacobi polynomials P (α,β)n (x) form a larger class of orthogonal polynomials than Gegenbauer polynomials C λn (x), Chebychev polynomials Tn (x) and Legendre polynomials. They can all be expressed in terms of Jacobi polynomials (see for example equations (8.962.2) and (8.962.3) in Gradshteyn and Ryzhikl)

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References

  1. I. S. Gradshteyn and I. N. Ryzhik. Tables of Integrals, Series and Products. London Academic, (1980).

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  2. R. H. Koornwinder, The addition formula for Jacobi polynomials, I summary of results. Indag. Math., 34: 179, (1972).

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  3. R. H. Koornwinder, The addition formula for Jacobi polynomials and spherical harmonics. SIAM J. Appt Math., 25: 236, (1973).

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  4. T. A. Antone, Expansion of Jacobi polynomials in terms of orthogonal functions. J. Phys. A, 26: 927, (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. E. D. Rainy Ile. Special Function, The Macmillan Company, New York, (1960).

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  6. J. Rasch. (e,2e) processes with neutral atom targets, Ph. D. thesis, University of Cambridge, (1996).

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  7. W. Magnus, F. Oberhettinger, and R. P. Soni. Formulas and Theorems for the Special Functions of Mathematical Physics. Springer Verlag, Berlin, Heidelberg, New York, (1966).

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  8. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricorni. Higher Transcendental Functions, Volume I. (1953).

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  9. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricorni. Higher Transcendental Functions, Volume II. (1953).

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, England

    J. Rasch

Authors
  1. J. Rasch
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Editor information

Editors and Affiliations

  1. University of Cambridge, Cambridge, England

    Colm T. Whelan

  2. The Queen’s University of Belfast, Belfast, Northern Ireland

    H. R. J. Walters

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© 1997 Springer Science+Business Media New York

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Rasch, J. (1997). On the Addition Theorem for Jacobi Polynomials. In: Whelan, C.T., Walters, H.R.J. (eds) Coincidence Studies of Electron and Photon Impact Ionization. Physics of Atoms and Molecules. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9751-0_23

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  • DOI: https://doi.org/10.1007/978-1-4757-9751-0_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9753-4

  • Online ISBN: 978-1-4757-9751-0

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