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A generalization of the extended Jacobi polynomials in two variables

Year 2015, Volume: 28 Issue: 3, 503 - 521, 05.10.2015

Abstract

References

  • Aktaş, R. "A note on multivariable Humbert matrix polynomials", Gazi University Journal of Science, 27 (2): 747-754, (2014).
  • Aktaş, R. and Altın, A., "A class of multivariable polynomials associated with Humbert Polynomials", Hacettepe Journal of Mathematics and Statistics, 42 (4): 359-372, (2013).
  • Aktaş, R., Altın, A. and Taşdelen, F., "A note on a family of two-variable polynomials", Journal of Computational and Applied Mathematics, 235: 4825- 4833, (2011).
  • Aktaş, R. and Erkuş-Duman, E., "The Laguerre polynomials
  • Slovaca, 63(3): 531-544, (2013). variables",
  • Mathematica [5] Aktaş, R. and Erkuş-Duman, E., "On a family of multivariate modified Humbert polynomials", The Scientific World Journal, 2013: 1-12, (2013).
  • Altın, A., Aktaş, R. and Erkuş-Duman, E. "On a multivariable extension for the extended Jacobi polynomials", J. Math. Anal. Appl. 353: 121-133, (2009).
  • Altın, A. and Erkuş, E., "On a multivariable extension of
  • Transform. Spec. Funct. 17: 239-244, (2006). polynomials",
  • Integral [8] Appell, P. and Kampé de Fériet, J., "Fonctions Hypergéométriques et Hyperspériques: Polynomes d'Hermite". Gauthier-Villars, Paris, (1926).
  • Bailey, W. N. , "Generalized Hypergeometric Series", Cambridge Math. Tract No. 32, Cambridge Univ. Press, Cambridge, (1935).
  • Carlitz, L., "An integral for the product of two Laguerre polynomials", Boll. Un. Mat. Ital. (3), 17 : 25- 28, (1962).
  • Dunkl, C.F., and Xu, Y., "Orthogonal polynomials of several variables", Cambridge Univ. press, New York, (2001).
  • Erkuş-Duman, E., Altın, A. and Aktaş, R., "Miscellaneous properties of some multivariable
  • polynomials", Mathematical and Computer Modelling, 54: 1875-1885, (2011).
  • Fujiwara, I., "A unified presentation of classical orthogonal polynomials", Math. Japon. 11: 133-148, (1966).
  • Koornwinder, T.H. , "Two variable analogues of the classical orthogonal polynomials. Theory and application of special functions", Acad. Press. Inc., New York, (1975).
  • Malave, P.B. and Bhonsle, B.R. , "Some recurrence relations and differential formulae for two-variable orthogonal polynomials 2
  • orthogonal over the unit disk", Ranchi Uni. Math. Jour. 9 : 45-52, (1978). P x, y
  • n,kx, y which are [16] Malave, P.B. and Bhonsle, B.R. , "Some recurrence relations and differential formulae for two variable orthogonal polynomials 2
  • orthogonal over the unit disk-I", Jour. Ind. Acad. Maths. 2: 31-35, (1980). P x, y
  • n,kx, y which are [17] Malave, P.B. and Bhonsle, B.R. , "Some generating functions of two variable analogue of Jacobi polynomials of class II", Ganita, 31 (1) : 29-37, (1980).
  • Rainville, E. D.,"Special Functions", The Macmillan Company, New York, (1960).
  • Singhal, B. M., "Integral representation for the product of two polynomials", Vijnana Parishad Anusandhan Patrica, 17: 165-169, (1974).
  • Suetin, P. K., "Orthogonal polynomials in two variables", Gordon and Breach Science Publishers, Moscow, (1988).
  • Szegö, G., "Orthogonal polynomials", Vol. 23, Amer. Math. Soc. Colloq. Publ., 4th ed., (1975).
  • Srivastava, H. M. and Manocha, H. L., "A Treatise on Generating Functions", Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1984).
Year 2015, Volume: 28 Issue: 3, 503 - 521, 05.10.2015

Abstract

References

  • Aktaş, R. "A note on multivariable Humbert matrix polynomials", Gazi University Journal of Science, 27 (2): 747-754, (2014).
  • Aktaş, R. and Altın, A., "A class of multivariable polynomials associated with Humbert Polynomials", Hacettepe Journal of Mathematics and Statistics, 42 (4): 359-372, (2013).
  • Aktaş, R., Altın, A. and Taşdelen, F., "A note on a family of two-variable polynomials", Journal of Computational and Applied Mathematics, 235: 4825- 4833, (2011).
  • Aktaş, R. and Erkuş-Duman, E., "The Laguerre polynomials
  • Slovaca, 63(3): 531-544, (2013). variables",
  • Mathematica [5] Aktaş, R. and Erkuş-Duman, E., "On a family of multivariate modified Humbert polynomials", The Scientific World Journal, 2013: 1-12, (2013).
  • Altın, A., Aktaş, R. and Erkuş-Duman, E. "On a multivariable extension for the extended Jacobi polynomials", J. Math. Anal. Appl. 353: 121-133, (2009).
  • Altın, A. and Erkuş, E., "On a multivariable extension of
  • Transform. Spec. Funct. 17: 239-244, (2006). polynomials",
  • Integral [8] Appell, P. and Kampé de Fériet, J., "Fonctions Hypergéométriques et Hyperspériques: Polynomes d'Hermite". Gauthier-Villars, Paris, (1926).
  • Bailey, W. N. , "Generalized Hypergeometric Series", Cambridge Math. Tract No. 32, Cambridge Univ. Press, Cambridge, (1935).
  • Carlitz, L., "An integral for the product of two Laguerre polynomials", Boll. Un. Mat. Ital. (3), 17 : 25- 28, (1962).
  • Dunkl, C.F., and Xu, Y., "Orthogonal polynomials of several variables", Cambridge Univ. press, New York, (2001).
  • Erkuş-Duman, E., Altın, A. and Aktaş, R., "Miscellaneous properties of some multivariable
  • polynomials", Mathematical and Computer Modelling, 54: 1875-1885, (2011).
  • Fujiwara, I., "A unified presentation of classical orthogonal polynomials", Math. Japon. 11: 133-148, (1966).
  • Koornwinder, T.H. , "Two variable analogues of the classical orthogonal polynomials. Theory and application of special functions", Acad. Press. Inc., New York, (1975).
  • Malave, P.B. and Bhonsle, B.R. , "Some recurrence relations and differential formulae for two-variable orthogonal polynomials 2
  • orthogonal over the unit disk", Ranchi Uni. Math. Jour. 9 : 45-52, (1978). P x, y
  • n,kx, y which are [16] Malave, P.B. and Bhonsle, B.R. , "Some recurrence relations and differential formulae for two variable orthogonal polynomials 2
  • orthogonal over the unit disk-I", Jour. Ind. Acad. Maths. 2: 31-35, (1980). P x, y
  • n,kx, y which are [17] Malave, P.B. and Bhonsle, B.R. , "Some generating functions of two variable analogue of Jacobi polynomials of class II", Ganita, 31 (1) : 29-37, (1980).
  • Rainville, E. D.,"Special Functions", The Macmillan Company, New York, (1960).
  • Singhal, B. M., "Integral representation for the product of two polynomials", Vijnana Parishad Anusandhan Patrica, 17: 165-169, (1974).
  • Suetin, P. K., "Orthogonal polynomials in two variables", Gordon and Breach Science Publishers, Moscow, (1988).
  • Szegö, G., "Orthogonal polynomials", Vol. 23, Amer. Math. Soc. Colloq. Publ., 4th ed., (1975).
  • Srivastava, H. M. and Manocha, H. L., "A Treatise on Generating Functions", Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1984).
There are 27 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Rabia Aktaş

Esra Erkuş Duman

Publication Date October 5, 2015
Published in Issue Year 2015 Volume: 28 Issue: 3

Cite

APA Aktaş, R., & Erkuş Duman, E. (2015). A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science, 28(3), 503-521.
AMA Aktaş R, Erkuş Duman E. A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science. October 2015;28(3):503-521.
Chicago Aktaş, Rabia, and Esra Erkuş Duman. “A Generalization of the Extended Jacobi Polynomials in Two Variables”. Gazi University Journal of Science 28, no. 3 (October 2015): 503-21.
EndNote Aktaş R, Erkuş Duman E (October 1, 2015) A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science 28 3 503–521.
IEEE R. Aktaş and E. Erkuş Duman, “A generalization of the extended Jacobi polynomials in two variables”, Gazi University Journal of Science, vol. 28, no. 3, pp. 503–521, 2015.
ISNAD Aktaş, Rabia - Erkuş Duman, Esra. “A Generalization of the Extended Jacobi Polynomials in Two Variables”. Gazi University Journal of Science 28/3 (October 2015), 503-521.
JAMA Aktaş R, Erkuş Duman E. A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science. 2015;28:503–521.
MLA Aktaş, Rabia and Esra Erkuş Duman. “A Generalization of the Extended Jacobi Polynomials in Two Variables”. Gazi University Journal of Science, vol. 28, no. 3, 2015, pp. 503-21.
Vancouver Aktaş R, Erkuş Duman E. A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science. 2015;28(3):503-21.