A generalization of the extended Jacobi polynomials in two variables

Yıl 2015, Cilt: 28 Sayı: 3, 503 - 521, 05.10.2015

Rabia Aktaş , Esra Erkuş Duman

Öz

Anahtar Kelimeler

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

Kaynakça

• 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).