Research Article
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Year 2019, Volume: 7 Issue: 2, 363 - 370, 15.10.2019

Nejla Özmen , Nihal Yılmaz

Abstract

References

  • [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.

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

Year 2019, Volume: 7 Issue: 2, 363 - 370, 15.10.2019

Nejla Özmen , Nihal Yılmaz

Abstract

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.

Keywords

Mittag-Leffler polynomials deformed Mittag-Leffler polynomials generating functions

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Nejla Özmen

Nihal Yılmaz This is me

Submission Date June 15, 2019
Acceptance Date July 18, 2019
Publication Date October 15, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Özmen, N., & Yılmaz, N. (2019). On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials. Konuralp Journal of Mathematics, 7(2), 363-370. https://izlik.org/JA52UM29HB
AMA 1.Özmen N, Yılmaz N. On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials. Konuralp J. Math. 2019;7(2):363-370. https://izlik.org/JA52UM29HB
Chicago Özmen, Nejla, and Nihal Yılmaz. 2019. “On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials”. Konuralp Journal of Mathematics 7 (2): 363-70. https://izlik.org/JA52UM29HB.
EndNote Özmen N, Yılmaz N (October 1, 2019) On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials. Konuralp Journal of Mathematics 7 2 363–370.
IEEE [1]N. Özmen and N. Yılmaz, “On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials”, Konuralp J. Math., vol. 7, no. 2, pp. 363–370, Oct. 2019, [Online]. Available: https://izlik.org/JA52UM29HB
ISNAD Özmen, Nejla - Yılmaz, Nihal. “On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials”. Konuralp Journal of Mathematics 7/2 (October 1, 2019): 363-370. https://izlik.org/JA52UM29HB.
JAMA 1.Özmen N, Yılmaz N. On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials. Konuralp J. Math. 2019;7:363–370.
MLA Özmen, Nejla, and Nihal Yılmaz. “On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials”. Konuralp Journal of Mathematics, vol. 7, no. 2, Oct. 2019, pp. 363-70, https://izlik.org/JA52UM29HB.
Vancouver 1.Özmen N, Yılmaz N. On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials. Konuralp J. Math. [Internet]. 2019 Oct. 1;7(2):363-70. Available from: https://izlik.org/JA52UM29HB
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