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Evaluation of Apostol–Euler Based Poly Daehee Polynomials

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Abstract

In the present paper, we study the new type of generating function of Apostol–Euler based poly Daehee polynomials. By making use of this generating function, we investigate some new and interesting identities for the Apostol–Euler based poly Daehee polynomials. We also derive some implicit summation formulae for Apostol–Euler based poly Daehee polynomials by applying the series manipulation techniques.

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References

  1. Carlitz, L.: A note on Bernoulli and Euler polynomials of the second kind. Scr. Math. 25, 323–330 (1961)

    MathSciNet  MATH  Google Scholar 

  2. Choi, J., Khan, N., Usman, T., Aman, M.: Certain unified polynomials. Integral Transforms Spec. Funct. 30(1), 28–40 (2019)

    Article  MathSciNet  Google Scholar 

  3. Dattoli, G., Lorenzutta, S., Cesarano, C.: Finite sums and generalized forms of Bernoulli polynomials. Rend. Math. 19, 385–391 (1999)

    MathSciNet  MATH  Google Scholar 

  4. Jolany, H., Aliabadi, M., Corcino, R.B., Darafsheh, M.R.: A note on multi poly-Euler numbers and Bernoulli polynomials. arXiv preprint arXiv:1401.2645 (2014)

  5. Kim, T.: On the multiple q-Genocchi and Euler numbers. Russ. J. Math. Phys. 15(4), 481–486 (2008)

    Article  MathSciNet  Google Scholar 

  6. Khan, W.A.: A new class of Hermite poly-Genocchi polynomials. J. Anal. Number Theory 4, 1–8 (2016)

    Google Scholar 

  7. Khan, W.A.: A note on Hermite-based poly-Euler and multi poly-Euler polynomials. Palest. J. Math 5, 17–26 (2016)

    Google Scholar 

  8. Khan, N.U., Usman, T.: A new class of Laguerre-based generalized Apostol polynomials. Faciculi Math. 57, 67–89 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Khan, N.U., Usman, T.: A new class of Laguerre poly-Bernoulli numbers and polynomial. Adv. Stud. Contemp. Math. 27, 229–241 (2017)

    MATH  Google Scholar 

  10. Khan, N.U., Usman, T., Aman, M.: Generating functions for Legendre-based poly-Bernoulli numbers and polynomials. Honam Math. J. 39, 217–231 (2017)

    MathSciNet  MATH  Google Scholar 

  11. Khan, N.U., Usman, T.: A new class of Laguerre-based poly-Euler and multi poly-Euler polynomials. J. Anal. Number Theory 4, 113–120 (2016)

    Article  Google Scholar 

  12. Khan, N., Usman, T., Choi, J.: A new class of generalized polynomials. Turk. J. Math. 42(3), 1366–1379 (2018)

    MathSciNet  MATH  Google Scholar 

  13. Khan, S., Nahid, T.: Finding non-linear differential equations and certain identities for the Bernoulli–Euler and Bernoulli–Genocchi numbers. SN Appl. Sci. 1(3), 217 (2019)

    Article  Google Scholar 

  14. Kim, D.S., Kim, T.: A study on the integral of the product of several Bernoulli polynomials. Rocky Mt. J. Math. 44(4), 1251–1263 (2014)

    Article  MathSciNet  Google Scholar 

  15. Kim, D.S., Kim, T.: Some identities involving Genocchi polynomials and numbers. Ars Comb. 121, 403–412 (2015)

    MathSciNet  MATH  Google Scholar 

  16. Kim, D.S., Kim, T., Lee, S.H., Seo, J.-J.: Higher order Daehee numbers and polynomials. Int. J. Math. Anal. 8(6), 273–283 (2014)

    Article  MathSciNet  Google Scholar 

  17. Kim, T., Kwon, H.I., Lee, S.H., Seo, J.J.: A note on poly-Bernoulli numbers and polynomials of the second kind. Adv. Differ. Equ. 2014(1), 219 (2014)

    Article  MathSciNet  Google Scholar 

  18. Komatsu, T., Luca, F.: Some relationships between poly-Cauchy numbers and poly Bernoulli numbers. Ann. Math. Inform. 41, 99–105 (2013)

    MathSciNet  MATH  Google Scholar 

  19. Luo, Q.M., Srivastava, H.M.: Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials. J. Math. Anal. Appl. 308(1), 290–302 (2005)

    Article  MathSciNet  Google Scholar 

  20. Luo, Q.M.: Apostol–Euler polynomials of higher order and the Gaussian hypergeometric function. Taiwan. J. Math. 10(4), 917–925 (2006)

    Article  MathSciNet  Google Scholar 

  21. Luo, Q.M.: Extension for the Genocchi polynomials and its Fourier expansions and integral representations. Osaka J. Math. 48, 291–309 (2011)

    MathSciNet  MATH  Google Scholar 

  22. Rainville, E.D.: Special Functions. The MacMillan Comp., New York (1960)

    MATH  Google Scholar 

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Correspondence to Mohd. Saif.

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Saif, M., Nadeem, R. Evaluation of Apostol–Euler Based Poly Daehee Polynomials. Int. J. Appl. Comput. Math 6, 1 (2020). https://doi.org/10.1007/s40819-019-0748-2

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  • DOI: https://doi.org/10.1007/s40819-019-0748-2

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