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SOME RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P(α,β)n(x)

  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Shine, Raj S.N. (Department of Mathematics, Central University of Kerala) ;
  • Rathie, Arjun K. (Department of Mathematics, Central University of Kerala)
  • Received : 2014.12.03
  • Accepted : 2015.01.05
  • Published : 2015.01.31

Abstract

We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

Keywords

References

  1. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  2. 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.

Cited by

  1. A FAMILY OF NEW RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS Pn(α,β)(x) vol.40, pp.1, 2015, https://doi.org/10.5831/hmj.2018.40.1.163