Generalization of Bateman Polynomials

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Asad Ali, Muhammad Zafar Iqbal, Bilal Anwer, Ather Mehmood

Abstract

In this paper, generalize the Bateman polynomials in terms of generalized hypergeometric function of the type pFp. Establish different forms of extended polynomials such as series expansion, generating functions and recurrence relations.

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References

  1. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
  2. G. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, 2004.
  3. G. Andrews, R. Askey and R. Roy. Special Functions, Cambridge University Press, 1999.
  4. S. B. Trickovic and M. S. Stankovic, On the orthogonality of classical orthogonal polynomials, Integral Transforms Spec. Funct., 14(2003), 129-138.
  5. R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15 (2007), 179-192.
  6. K. Y. Chen and H. M. Srivastava, A limit relationship between Laguerre and Hermite polynomials. Integral Transforms Spec. Funct., 16(2005), 75 - 80.
  7. E. H. Doha, H. M. Ahmed and S. I. El-Soubhy, Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals, Integral Transforms Spec. Funct., 20 (2009), 491 - 503.
  8. I. Krasikov and A. Zarkh, Equioscillatory property of the Laguerre polynomials, J. Approx. Theory, 162(2010), 2021 - 2047.
  9. S. Alam and A. K. Chongdar, On generating functions of modified Laguerre polynomials, Rev. Real Academia de Ciencias. Zaragoza, 62(2007), 91 - 98.
  10. M. A. Khan and A. K. Shukla, On some generalized Sister Celines polynomials, Czechoslovak Math. J., 49(3) (1999), 527-545.
  11. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, HalstedPress (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.