On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials

Yıl 2019, Cilt: 7 Sayı: 2, 363 - 370, 15.10.2019

Nejla Özmen Nihal Yılmaz

Öz

The present study deals with some new properties for the Mittag-Leffler polynomials and the deformed Mittag-Leffler polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties and also some special cases for these polynomials.

Anahtar Kelimeler

Mittag-Leffler polynomials, deformed Mittag-Leffler polynomials, generating functions

Kaynakça

• [1] H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
• [2] G. Mittag-Leffler, Sur la repr´esentasion analytique des int´egrales et des invariants d’une ´equation diff´erentielle lin´eaire et homog´ene, Acta Math., 15 (1891), 1-32.
• [3] H. Bateman, The polynomial of Mittag–Leffler, Proc N.A.S. 26 (1940), 491-496.
• [4] H. Bateman, An orthogonal property of the hypergeometric polynomial, Proc N.A.S. 28 (1942), 374-377.
• [5] M.S. Stankovi´c, S.D. Marinkovi´c, P.M. Rajkovi´c, Deformed exponential functions of two variables, ArXiv 1005.5040v1, May 27, 2010. http://arxiv.org/abs/1005.5040v1.
• [6] S. Roman,The umbral calculus, Dover Publ. Inc. New York, 2005.
• [7] T.X. He, L.C. Hsu, P.J.-S. Shiue, The Sheffer group and the Riordan group, Discrete Applied Mathematics 155 (2007), 1895-1909.
• [8] A. Luzon, M.A. Moron, Recurrence relations for polynomial sequences via Riordan matrices, Linear Algebra and its Applications, 433 (2010), 1422-1446.
• [9] N. Ozmen, E. Erkus-Duman, Some results for a family of multivariable polynomials, AIP Conference Proceedings, 1558(2013), 1124-1127.
• [10] E. Erkus¸ and H.M. Srivastava, A unified presentation of some families of multivariable polynomials, Integral Transform Spec. Funct. 17 (2006), 267-273.
• [11] A. Altın, E. Erkus, On a multivariable extension of the Lagrange-Hermite polynomials. Integral Transform. and Spec. Funct. 17 (2006), 239-244.
• [12] D. S. Kim, T. Kim, T. Mansour and J.-J. Seo, Degenerate Mittag-Leffler Polynomials, Applied Mathematics and Computation, 274 (2016), 258-266.