DOI QR코드

DOI QR Code

BILINEAR AND BILATERAL GENERATING FUNCTIONS OF HEAT TYPE POLYNOMIALS SUGGESTED BY JACOBI POLYNOMIALS

Khan, Mumtaz Ahmad;Khan, Abdul Hakim;Singh, Manoj

  • Received : 2010.07.19
  • Published : 2011.10.31

Abstract

The present paper deals with generalization of several families of bilinear and bilateral generating functions for the heat type polynomials suggested by Jacobi polynomials with different argument.

Keywords

Laguerre polynomials;Rice polynomials;Gauss hypergeometric function;Appell's functions;Kamp$\acute{e}$ de F$\acute{e}$riet's double hypergeometric function;Lauricella's functions;Saran's functions

References

  1. M. A. Khan, A. H. Khan, and M. Singh, A note on heat type polynomials suggested by Jacobi polynomials, Communicated for publication.
  2. M. A. Khan, A. H. Khan, and M. Singh, Linear, bilinear and trilinear generating functions for heat type polynomials suggested by Jacobi polynomils, Communicated for publication.
  3. E. D. Rainville, Special Functions, MacMillan, New York, 1960, reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  4. S. Saran, Hypergeometric functions of three variables, Ganita 5 (1954), 77-91.
  5. B. L. Sharma and H. L. Manocha, Some generating functions of Jacobi polynomials, Mat. Vesnik 6(21) (1969), 403-407.
  6. H. M. Srivastava, A class of bilateral generating functions for the Jacobi polynomials, J. Korean Math. Soc. 8 (1971), 25-30.
  7. H. M. Srivastava, Generalized Neumann expansion involving hypergeometric functions, Proc. Cambridge Philos. Soc. 63 (1967), 425-429. https://doi.org/10.1017/S0305004100041359
  8. H. M. Srivastava and M. C. Daoust, Some generating functions for the Jacobi polyno- mials, Comment. Math. Univ. St. Paul. 20 (1971), 15-21.
  9. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and sons, New York, Chichester Brisbane, Toronto, 1984.
  10. H. M. Srivastava and J. P. Singhal, Certain generating functions for Jacobi, Laguerre, and Rice polynomials, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 355-363.