A note on Shively’s Pseudo-Laguerre Polynomials

A note on Shively’s Pseudo-Laguerre Polynomials

In this research, we esteblish some properties for the Shively’s Pseudo-Laguerre polynomials. We derive various families of multilinear and multilateral generating functions for a family of Shively’s Pseudo-Laguerre polynomials.

___

  • [1] R. L. Shively, On pseudo-Laguerre polynomials, Michigan thesis;1953.
  • [2] E. D. Rainville, Special Function, Macmillan, New York, 1960.
  • [3] H. L. Srivastava, L. Shy-Der, L. Shuoh-Jung, L. Han-Chun, Integral representations for the Lagrange polynomials, Shivelys pseudo-Laguerre polynomials, and the generalized Bessel polynomials, Russ. J. Math. Phys., 19 (1) (2012), 121-130.
  • [4] R. K. Jana, I. A. Salehbhai, A. K. Shukla, Shivleys polynomials of two variables, Int. J. of Math. Anal., 6 (36) (2012), 1757-1762.
  • [5] T. Letterio, Funzioni generatrici di particolari polinomi di Laguerre e de altri da essi dipendenti, Boll. Un. Mat. Ital. Ser.3, 7 (2) (1952), 160-167.
  • [6] M. A. Khan, A. H. Khan, S. M. Abbas, A note on pseudo Jacobi polynomials, Ain Shams Eng. J., 4 (2013), 127-131.
  • [7] H. M. Srivastava, H. L. Manocha, A Treatise on Generating Functions, Halsted Press, John Wiley and Sons, New York, 1984.
  • [8] E. Erkus-Duman, A. Altın, R. Aktas, Miscellaneous properties of some multivariable polynomials, Math. Comput. Modelling, 54 (2011), 1875-1885.
  • [9] R. Aktas, A. Altın, B. Cekim, On a two-variable analogue of Bessel functions, Journal of Inequalities and Special Functions, 3 (4) (2012), 13-23.
  • [10] N. Ozmen, E. Erkus-Duman, Some results for a family of multivariable polynomials, AIP Conf. Proc., 1558 (2013), 1124-1127.
  • [11] A. Altın, E. Erkus, On a multivariable extension of the Lagrange-Hermite polynomials, Integral Transform. Spec. Funct., 17 (4) (2006), 239-244.
  • [12] N. Ozmen, Some new properties of the Meixner polynomials, Sakarya Univ. J. Sci., 21 (6) (2017), 1454-1462.