Skip to main content
SpringerLink
Log in

Differential equations arising from polynomials of derangements and structure of their zeros

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we introduce the polynomials of derangements. We study differential equations arising from the generating functions of the polynomials of derangements. We also give explicit identities for the polynomials of derangements. Finally, we investigate the structure of zeros of the polynomials of derangements by using computer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Clarke, R.J., Sved, M.: Derangements and Bell numbers. Math. Mag. 66(5), 299–303 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Comtet, L.: Advanced Combinatorics: The Art of Finite and Infinite Expansions. D. Reidel Publishing Co., Boston (1974)

    Book  MATH  Google Scholar 

  3. Kim, M.S., Hu, S.: On p-adic Hurwitz-type Euler zeta functions. J. Number Theory 132, 2977–3015 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kim, Y.H., Jung, H.Y., Ryoo, C.S.: On the generalized Euler polynomials of the second kind. J. Appl. Math. Inform. 31(5–6), 623–630 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kim, T., Kim, D.S., Ryoo, C.S., Kwon, H.I.: Differential equations associated with Mahler and Sheffer-Mahler polynomials. Submitted for publication

  6. Ozden, H., Simsek, Y.: A new extension of q-Euler numbers and polynomials related to their interpolation functions. Appl. Math. Lett. 21, 934–938 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ryoo, C.S.: A numerical investigation on the zeros of the tangent polynomials. J. Appl. Math. Inform. 32(3–4), 315–322 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ryoo, C.S.: Differential equations associated with tangent numbers. J. Appl. Math. Inform. 34(5–6), 487–494 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ryoo, C.S.: A numerical investigation on the structure of the roots of q-Genocchi polynomials. J. Appl. Math. Comput. 26, 325–332 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Simsek, Y.: Complete sum of products of (h, q)-extension of Euler polynomials and numbers. J. Differ. Equ. Appl. 16(11), 1331–1348 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Young, P.T.: Degenerate Bernoulli polynomials, generalized factorial sums, and their applications. J. Number Theory 128, 738–758 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hannam University, Daejeon, 306-791, Korea

    Cheon Seoung Ryoo

Authors
  1. Cheon Seoung Ryoo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheon Seoung Ryoo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ryoo, C.S. Differential equations arising from polynomials of derangements and structure of their zeros. J. Appl. Math. Comput. 56, 533–545 (2018). https://doi.org/10.1007/s12190-017-1085-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-017-1085-4

Keywords

Mathematics Subject Classification

Search

Navigation