A generalization of the extended Jacobi polynomials in two variables

Rabia Aktaş, Esra Erkuş Duman
1.910 726

Abstract



Keywords


Extended Jacobi polynomials, Jacobi polynomials, recurrence relation,generating function, hypergeometric function.

Full Text:

PDF

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).