Advertisement

Boletín de la Sociedad Matemática Mexicana

, Volume 21, Issue 2, pp 149–162 | Cite as

More properties on multi-poly-Euler polynomials

  • Hassan Jolany
  • Roberto B. Corcino
  • Takao Komatsu
Original Article

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.

Keywords

Poly-Euler polynomials Appell polynomials Poly-logarithm Generating function 

Mathematics Subject Classification

11B68 11B73 05A15 

References

  1. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bayad, A., Hamahota, Y.: Arakawa-Kaneko \(L\)-functions and generalized poly-Bernoulli polynomials. J. Number Theory 131, 1020–1036 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bayad, A., Hamahota, Y.: Multiple polylogarithms and multi-poly-Bernoulli polynomials. Funct. Approx. Comment. Math. 46(1), 45–61 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bayad, A., Hamahota, Y.: Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65, 15–24 (2011)Google Scholar
  5. 5.
    Beńyi, B.: Advances in Bijective Combinatorics. Ph.D. Thesis, University of Szeged, Hungary (2014)Google Scholar
  6. 6.
    Brewbaker, C.: A combinatorial interpretation of the poly-Bernoulli numbers and two fermat analogues. Integers 8(1), #A02 (2008)Google Scholar
  7. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Comtet, L.: Advanced Combinatorics. D. Reidel Publishing Company, Dordrecht (1974)CrossRefzbMATHGoogle Scholar
  9. 9.
    Coppo, M.-A., Candelpergher, B.: The Arakawa-Kaneko zeta function. Ramanujan J. 22, 153–162 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hamahota, Y., Masubuchi, H.: Special multi-poly-Bernoulli numbers. J. Integer Seq. 10 (2007)Google Scholar
  11. 11.
    Hamahata, Y.: Poly-Euler polynomials and Arakawa-Kaneko type zeta functions. Funct. Approx. Comment. Math. 51(1), 7–22 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)zbMATHGoogle Scholar
  13. 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. 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. 15.
    Kaneko, M.: Poly-Bernoulli numbers. J. Theor. Nr. Bordx. 9, 221–228 (1997)Google Scholar
  16. 16.
    Lee, D.W.: On multiple Appell polynomials. Proc. Am. Math. Soc. 139(6), 2133–2141 (2011)CrossRefzbMATHGoogle Scholar
  17. 17.
    Ohno, Y., Sasaki, Y.: On the parity of poly-Euler numbers. RIMS Kokyuroku Bessatsu B 32, 271–278 (2012)Google Scholar
  18. 18.
    Shohat, J.: The relation of the classical orthogonal polynomials to the polynomials of Appell. Am. J. Math. 58, 453–464 (1936)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Toscano, L.: Polinomi Ortogonali o Reciproci di Ortogonali Nella classe di Appell. Lect. Mat. 11, 168–174 (1956)MathSciNetGoogle Scholar

Copyright information

© Sociedad Matemática Mexicana 2015

Authors and Affiliations

  • Hassan Jolany
    • 1
  • Roberto B. Corcino
    • 2
  • Takao Komatsu
    • 3
  1. 1.Laboratoire Paul Painlevé, UFR de MathématiquesUniversité des Sciences et Technologies de Lille, CNRS-UMR 8524Villeneuve d’Ascq CedexFrance
  2. 2.Mathematics and ICT DepartmentCebu Normal UniversityCebuPhilippines
  3. 3.School of Mathematics and Statistics, Wuhan UniversityWuhanChina

Personalised recommendations