Abstract
This article deals with the introduction of truncated exponential-based Mittag-Leffler polynomials and derivation of their properties. The operational correspondence between these polynomials and Mittag-Leffler polynomials is established. An integral representation for these polynomials is also derived.
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Andrews L.C.: Special Functions for Engineers and Applied Mathematicians. Macmillan, New York (1985)
Appell P.: Sur une classe de polynômes. Ann. Sci. Ecole. Norm. Sup. 9(2), 119–144 (1880)
Bateman H.: The polynomials of Mittag-Leffler. Proc. NAS 26, 491–496 (1940)
Bateman H.: An orthogonal property of the hypergeometric polynomial. Proc. NAS 28, 374–377 (1942)
Dattoli, G: Hermite–Bessel and Laguerre–Bessel functions: a by-product of the monomiality principle. In: Advanced Special Functions and Applications (Melfi, 1999). Proceedings of the Melfi School on Advanced Topics in Mathematics and Physics, vol. 1, Aracne, Rome, pp. 147–164 (2000)
Dattoli G., Cesarano C., Sacchetti D.: A note on truncated polynomials. Appl. Math. Comput. 134, 595–605 (2003)
Dattoli G., Migliorati M., Srivastava H.M.: A class of Bessel summation formulas and associated operational methods. Fract. Calc. Appl. Anal. 7(2), 169–176 (2004)
Dattoli G., Ottaviani P.L., Torre A., Vázquez L.: Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cimento Soc. Ital. Fis. 20(2), 1–133 (1997)
Gould H.W., Hopper A.T.: Operational formulas connected with two generalization of Hermite polynomials. Duke Math. J. 29, 51–63 (1962)
Khan S., Riyasat M.: Determinantal approach to certain mixed special polynomials related to Gould–Hopper polynomials. Appl. Math. Comput. 251, 599–614 (2015)
Khan S., Yasmin G., Ahmad N.: On a new family related to truncated exponential and Sheffer polynomials. J. Math. Anal. Appl. 418, 921–937 (2014)
Paris R.B.: The asymptotic of the Mittag-Leffler polynomials. J. Class. Anal. 1(1), 1–16 (2012)
Rainville, E.D.: Special Functions. Macmillan, New York (1960) [Reprinted by Chelsea Publ. Co., Bronx, New York, 1971]
Roman S.: The Umbral Calculus. Academic Press, New York (1984)
Rzadkowski, G.: On some expansions, involving falling factorials, for the Euler gamma function and the Riemann zeta function (2010). arXiv:1007.1955v1
Srivastava, H.M., Manocha, H.L.: A treatise on generating functions. In: Ellis Horwood Series: Mathematics and Its Applications. Ellis Horwood Ltd./Halsted Press (Wiley), Chichester/New York (1984)
Stankovic, M.S., Marinkovic, S.D., Rajkovic, P.M.: Deformed Mittag-Leffler polynomials (2010). arXiv:1007.3612v1
Steffensen J.F.: The poweroid, an extension of the mathematical notion of power. Acta Math. 73, 333–366 (1941)
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This work has been done under Post-Doctoral Fellowship (Office Memo No. 2/40/14/2012/ R&D-II/8125) awarded to N. Ahmad by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai.
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Yasmin, G., Khan, S. & Ahmad, N. Operational Methods and Truncated Exponential-Based Mittag-Leffler Polynomials. Mediterr. J. Math. 13, 1555–1569 (2016). https://doi.org/10.1007/s00009-015-0610-7
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DOI: https://doi.org/10.1007/s00009-015-0610-7