Erkuş-Duman, Esra; Altın, Abdullah; Aktaş, Rabïa Miscellaneous properties of some multivariable polynomials. (English) Zbl 1235.33012 Math. Comput. Modelling 54, No. 9-10, 1875-1885 (2011). Summary: We present various integral representations for the Chan-Chyan-Srivastava, Lagrange-Hermite, Erkus-Srivastava multivariable polynomials and extended Jacobi polynomials. Then, we obtain some partial differential equations for the product of any two of them. We show that the Chan-Chyan-Srivastava multivariable polynomials are not orthogonal. We also discuss other miscellaneous properties of the Chan – Chyan – Srivastava, Lagrange – Hermite and Erkus – Srivastava multivariable polynomials. Cited in 4 Documents MSC: 33C70 Other hypergeometric functions and integrals in several variables 26C05 Real polynomials: analytic properties, etc. Keywords:Chan-Chyan-Srivastava multivariable polynomials; Lagrange-Hermite multivariable polynomials; Erkus-Srivastava multivariable polynomials; extended Jacobi polynomials; integral representation; recurrence relation PDFBibTeX XMLCite \textit{E. Erkuş-Duman} et al., Math. Comput. Modelling 54, No. 9--10, 1875--1885 (2011; Zbl 1235.33012) Full Text: DOI References: [1] Chan, W.-C. C.; Chyan, C.-J.; Srivastava, H. M., The Lagrange polynomials in several variables, Integral Transforms Spec. Funct., 12, 139-148 (2001) · Zbl 1057.33003 [2] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G., Higher Transcendental Functions, vol. III (1955), McGraw-Hill Book Company: McGraw-Hill Book Company New York, Toronto and London · Zbl 0064.06302 [3] Altın, A.; Erkuş, E., On a multivariable extension of the Lagrange-Hermite polynomials, Integral Transforms Spec. Funct., 17, 239-244 (2006) · Zbl 1095.33003 [4] Erkuş, E.; Srivastava, H. M., A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct., 17, 267-273 (2006) · Zbl 1098.33016 [5] Fujiwara, I., A unified presentation of classical orthogonal polynomials, Math. Japon., 11, 133-148 (1966) · Zbl 0154.06402 [6] Szegö, G., Orthogonal Polynomials, vol. 23 (1975), Amer. Math. Soc. Colloq. Publ · JFM 65.0278.03 [7] Pittaluga, G.; Sacripante, L.; Srivastava, H. M., Some families of generating functions for the Jacobi and related orthogonal polynomials, J. Math. Anal. Appl., 238, 385-417 (1999) · Zbl 0944.33008 [8] Srivastava, H. M.; Manocha, H. L., A Treatise on Generating Functions (1984), Halsted Press, Ellis Horwood Limited, Chichester, John Wiley and Sons: Halsted Press, Ellis Horwood Limited, Chichester, John Wiley and Sons New York · Zbl 0535.33001 [9] Srivastava, H. M.; Panda, R., An integral representation for the product of two Jacobi polynomials, J. Lond. Math. Soc., 12, 419-425 (1975) · Zbl 0304.33015 [10] Krall, H. L.; Sheffer, I. M., Orthogonal polynomials in two variables, Ann. Mat. Pura Appl., 76, 4, 325-376 (1967) · Zbl 0186.38602 [11] Suetin, P. K., Orthogonal Polynomials in Two Variables (1988), Gordon and Breach Science Publishers: Gordon and Breach Science Publishers Moscow · Zbl 0658.33004 [12] Rainville, E. D., Special Functions (1960), The Macmillan Company: The Macmillan Company New York · Zbl 0050.07401 [13] Altın, A.; Aktaş, R.; Erkuş-Duman, E., On a multivariable extension for the extended Jacobi polynomials, J. Math. Anal. Appl., 353, 121-133 (2009) · Zbl 1172.33002 [14] Dattoli, G.; Ricci, P. E.; Cesarano, C., The Lagrange polynomials, the associated generalizations, and the umbral calculus, Integral Transforms Spec. Funct., 14, 181-186 (2003) · Zbl 1032.33007 [15] Lee, D. W., Partial differential equations for products of two classical orthogonal polynomials, Bull. Korean Math. Soc., 42, 179-188 (2005) · Zbl 1077.33017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.