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A FAMILY OF NEW RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS Pn(α,β)(x)

  • Shine, Raj S.N. (Department of Mathematics, Central University of Kerala) ;
  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Rathie, Arjun K. (Department of Mathematics, Central University of Kerala)
  • Received : 2017.12.11
  • Accepted : 2018.02.18
  • Published : 2018.03.25

Abstract

The objective of this paper is to present 87 recurrence relations for the Jacobi polynomials $P_n^{({\alpha},{\beta})}(x)$. The results presented here most of which are presumably new are obtained with the help of Gauss's fifteen contiguous function relations and some other identities recently recorded in the literature.

Keywords

Recurrence relations;Jacobi polynomials;Hypergeometric function $_2F_1$;Contiguous function relations;Gamma function;Pochhammer symbol

References

  1. Y. J. Cho, T. Y. Seo and J. Choi, Note on contiguous function relations, East. Asian Math. J. 15(1) (2001), 29-38.
  2. J. Choi, S. N. Shine Raj and A. K. Rathie, Some recurrence relations for the Jacobi polynomials $P^{({\alpha},{\beta})}_n$ (x), East. Asian Math. J. 31(1) (2015), 103-107. https://doi.org/10.7858/eamj.2015.010
  3. C. F. Gauss, Disquisitiones generaler circa seriem infinitam, Gottingen thesis (1812), Comment Soc. Reg. Sci., Gottingensis Recent, 2 (Reprint) in Carl Fredrich Gauss Werke, 12 Vols., Vol. 3, 123-162 (see also 207-230), Gottingen, (1870-1933).
  4. Y. S. Kim, S. N. Shine Raj and A. K. Rathie, A note on two recurrence relations for the Jacobi polynomials, submitted for publication, (2015).
  5. M. A. Rakha, A. K. Rathie and P. Chopra, On some new contiguous relations for the Gauss hypergeometric functions with applications, Comput. Math. Appl. 61 (2011), 620-629. https://doi.org/10.1016/j.camwa.2010.12.008
  6. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  7. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.