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On some families of new constructed polynomials. (English) Zbl 1435.33003

Summary: The purpose of this paper is to introduce some new polynomials obtained from second- and third-order algebraic equations by using a simple iterative method. One-variable polynomials obtained in this study deal with special form of Pöschl-Teller potential with constant energy, and the two-variable polynomials are related to time-dependent wave equations. We present some recurrence relations, Binet formula and get various families of linear, multilinear and multilateral generating functions for these polynomials. In addition, we derive some special cases. At the end of the paper we also give an extension to the multidimensional case of our results.

MSC:

33C05 Classical hypergeometric functions, \({}_2F_1\)
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[1] Ciftci, H.; Hall, Rl; Saad, N., Asymptotic iteration method for eigenvalue problems, J. Phys. A Math. Gen., 36, 11807-11816 (2003) · Zbl 1070.34113
[2] Chen, K-Y; Liu, S-J; Srivastava, Hm, Some new results for the Lagrange polynomials in several variables, ANZIAM J., 49, 243-258 (2007) · Zbl 1148.33002
[3] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, Fg, Higher Transcendental Functions (1955), New York: McGraw-Hill, New York · Zbl 0064.06302
[4] Erkus-Duman, E., Matrix extensions of polynomials in several variables, Util. Math., 85, 161-180 (2011) · Zbl 1293.15009
[5] Erkus-Duman, E.; Altın, E.; Aktas, R., Miscellaneous properties of some multivariable polynomials, Math. Comput. Model., 54, 1875-1885 (2011) · Zbl 1235.33012
[6] Ozmen, N.; Erkus-Duman, E., Some families of generating functions for the generalized Cesáro polynomials, J. Comput. Anal. Appl., 25, 670-683 (2018)
[7] Ozmen, N.; Erkus-Duman, E., Some results for a family of multivariable polynomials, AIP Conf. Proc., 1558, 1124-1127 (2013)
[8] Rainville, Ed, Special Functions (1960), New York: Macmillan, New York
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