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More properties on multi-poly-Euler polynomials

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Abstract

In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly-Euler polynomials. Moreover, we introduce a more general form of multi-poly-Euler polynomials and obtain some identities parallel to those of the generalized poly-Euler polynomials.

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References

  1. Araci, S., Acikgoz, M., Sen, E.: On the extended Kims \(p\)-adic \(q\)-deformed fermionic integrals in the p-adic integer ring. J. Number Theory 133(10), 3348–3361 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bayad, A., Hamahota, Y.: Arakawa-Kaneko \(L\)-functions and generalized poly-Bernoulli polynomials. J. Number Theory 131, 1020–1036 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bayad, A., Hamahota, Y.: Multiple polylogarithms and multi-poly-Bernoulli polynomials. Funct. Approx. Comment. Math. 46(1), 45–61 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bayad, A., Hamahota, Y.: Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65, 15–24 (2011)

  5. Beńyi, B.: Advances in Bijective Combinatorics. Ph.D. Thesis, University of Szeged, Hungary (2014)

  6. Brewbaker, C.: A combinatorial interpretation of the poly-Bernoulli numbers and two fermat analogues. Integers 8(1), #A02 (2008)

  7. Candelpergher, B., Coppo, M.A.: A new class of identities involving Cauchy numbers, harmonic numbers and zeta values. Ramanujan J. 27(3), 305–328 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Comtet, L.: Advanced Combinatorics. D. Reidel Publishing Company, Dordrecht (1974)

    Book  MATH  Google Scholar 

  9. Coppo, M.-A., Candelpergher, B.: The Arakawa-Kaneko zeta function. Ramanujan J. 22, 153–162 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hamahota, Y., Masubuchi, H.: Special multi-poly-Bernoulli numbers. J. Integer Seq. 10 (2007)

  11. Hamahata, Y.: Poly-Euler polynomials and Arakawa-Kaneko type zeta functions. Funct. Approx. Comment. Math. 51(1), 7–22 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jolany, H., Alikelaye, R.E., Mohamad, S.S.: Some results on the generalization of Bernoulli, Euler and Genocchi polynomials. Acta Univ. Apulensis Math. Inform. 27, 299–306 (2011)

    MATH  Google Scholar 

  13. Jolany, H., Aliabadi, M., Corcino, R.B., Darafsheh, M.R.: A note on multi poly-Euler numbers and Bernoulli polynomials. Gen. Math. 20(2–3), 122–134 (2012)

    Google Scholar 

  14. Jolany, H., Darafsheh, M.R., Alikelaye, R.E.: Generalizations of poly-Bernoulli numbers and polynomials. Int. J. Math. Comb. 2, 7–14 (2010)

    Google Scholar 

  15. Kaneko, M.: Poly-Bernoulli numbers. J. Theor. Nr. Bordx. 9, 221–228 (1997)

  16. Lee, D.W.: On multiple Appell polynomials. Proc. Am. Math. Soc. 139(6), 2133–2141 (2011)

    Article  MATH  Google Scholar 

  17. Ohno, Y., Sasaki, Y.: On the parity of poly-Euler numbers. RIMS Kokyuroku Bessatsu B 32, 271–278 (2012)

  18. Shohat, J.: The relation of the classical orthogonal polynomials to the polynomials of Appell. Am. J. Math. 58, 453–464 (1936)

    Article  MathSciNet  Google Scholar 

  19. Toscano, L.: Polinomi Ortogonali o Reciproci di Ortogonali Nella classe di Appell. Lect. Mat. 11, 168–174 (1956)

    MathSciNet  Google Scholar 

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Correspondence to Hassan Jolany.

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Jolany, H., Corcino, R.B. & Komatsu, T. More properties on multi-poly-Euler polynomials. Bol. Soc. Mat. Mex. 21, 149–162 (2015). https://doi.org/10.1007/s40590-015-0061-y

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  • DOI: https://doi.org/10.1007/s40590-015-0061-y

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