충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제25권2호
  • /
  • Pages.253-265
  • /
  • 2012
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

$q$-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN TWO VARIABLES

  • 발행 : 2012.05.15
⟨ 이전 논문 다음 논문 ⟩

초록

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subse- quently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}_{n}^{m}(\cdot)$. Here, we aim at defining a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}_{n}^{2}(\cdot)$ and presenting their several generating functions.

키워드

참고문헌

  1. J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), 781-789. https://doi.org/10.4134/CKMS.2003.18.4.781
  2. J. Choi, A generalization of Gottlieb polynomials in several variables, Appl. Math. Lett. 25 (2012), 43-46. https://doi.org/10.1016/j.aml.2011.07.006
  3. G. Gasper and M. Rahman, Basic Hypergeometric Series (with a Foreword by Richard Askey), Encyclopedia of Mathematics and Its Applications, Vol. 35, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne and Sydney, 1990.
  4. G. Gasper and M. Rahman, Basic Hypergeometric Series (with a Foreword by Richard Askey), Second edition, Encyclopedia of Mathematics and Its Applications, Vol. 96, Cambridge University Press, Cambridge, London and New York, 2004.
  5. M. J. Gottlieb, Concerning some polynomials orthogonal on a finite or enu- merable set of points, Amer. J. Math. 60(2) (1938), 453-458. https://doi.org/10.2307/2371307
  6. M. A. Khan and M. Akhlaq, Some new generating functions for Gottlieb poly- nomials of several variables, Internat. Trans. Appl. Sci. 1(4) (2009), 567-570.
  7. M. A. Khan and M. Asif, A note on generating functions of q-Gottlieb polyno- mials, Commun. Korean Math. Soc. (2011), Accepted for publication.
  8. G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ. Mat. Palermo 7 (1893), 111-158. https://doi.org/10.1007/BF03012437
  9. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960.
  10. E. D. Rainville, Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  11. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1985.
  12. 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, and Toronto, 1984.

피인용 문헌

  1. FORMULAS DEDUCIBLE FROM A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES vol.34, pp.4, 2012, https://doi.org/10.5831/HMJ.2012.34.4.603
  2. q-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN THREE VARIABLES vol.34, pp.3, 2012, https://doi.org/10.5831/HMJ.2012.34.3.327
  3. Gottlieb Polynomials and Their q-Extensions vol.9, pp.13, 2012, https://doi.org/10.3390/math9131499