Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 9 Sayı: 1, 1 - 8, 01.03.2021
https://doi.org/10.36753/mathenot.839111

Öz

Kaynakça

  • [1] Bayad, A., Hamahata, Y.: Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65, 15-24 (2012).
  • [2] Carlitz, L.: Degenerate Stirling, Bernoulli and Eulerian numbers. Utilitas Math. 15, 51-88 (1979).
  • [3] Chung, S.-K., Jang, G.-W., Kim, D.S., Kwon, J.: Some identities of the type 2 degenerate Bernoulli and Euler numbers. Adv. Stud. Contemp. Math. (Kyungshang). 29 (4), 613-632 (2019).
  • [4] Duran, U., Acikgoz, M., Araci, S.: Hermite based poly-Bernoulli polynomials with a q parameter, Adv. Stud. Contemp. Math. (Kyungshang). 28 (2), 285-296 (2018).
  • [5] Kaneko, M.: poly-Bernoulli numbers. J. Theor. Nombres Bordx. 9, 221-228 (1997).
  • [6] Kumar Sharma, S., Khan,W.A., Araci, S., Ahmed, S.S.: New type of degenerate Daehee polynomials of the second kind. Adv. Differ. Equ. 428 (2020).
  • [7] Sharma, S.K., Khan, W.A., Araci, S., Ahmed, S.S.: New construction of type 2 degenerate central Fubini polynomials with their certain properties. Adv. Differ. Equ. 587 (2020).
  • [8] Kilar, N., Simsek, Y.: Relations on Bernoulli and Euler polynomials related to trigonometric functions. Adv. Stud. Contemp. Math. (Kyungshang). 29 (2), 191-198 (2019).
  • [9] Kim, T., Kim, D.S., Kwon, J., Lee, H.: Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials. Adv. Differ. Equ. 168 (2020).
  • [10] Kim, T., Jang, Y.S; Seo, J.J: A note on Poly-Genocchi numbers and polynomials. Appl. Math. Sci. 8 (96), 4775-4781 (2014).
  • [11] Kim, T., Kim, D.S.: A note on type 2 Changhee and Daehee polynomials. RACSAM. 113, 2783-2791 (2019).
  • [12] Kim, D.S., Kim, T.: A note on degenerate poly-Bernoulli numbers and polynomials. Adv. Differ. Equ. 258 (2015).
  • [13] Kim, T., Kim, D.S., Kim, H.Y., Jang, L.-C.: Degenerate poly-Bernoulli numbers and polynomials. Informatica. 31 (3), 2-8 (2020).
  • [14] Kim, T., Jang, L.-C., Kim, D. S., Kim, H. Y.: Some identities on type 2 degenerate Bernoulli polynomials of the second kind. Symmetry. 12 (4), 510 (2020).
  • [15] Kim, D.S., Kim, T., Ryoo, C.S.: Generalized type 2 degenerate Euler numbers. Adv. Stud.Contemp. Math. (Kyungshang). 30 (2), 165-169, (2020).
  • [16] Kwon, J., Kim,W.J., Rim, S.-H.: On the some identities of the type 2 Daehee and Changhee polynomials arising from p-adic integrals on Zp. Proc. Jangjeon Math. Soc. 22 (3), 487-497 (2019).
  • [17] Kwon, J., Jang, L.-C.: A note on type 2 poly-Apostol-Bernoulli polynomials. Adv. Stud. Contemp. Math. (Kyungshang). 30 (2), 253-262 (2020).
  • [18] Lee, D.S., Kim, H.K., Jang, L.-C.: Type 2 degenerate poly-Euler Polynomials. Symmetry. 12, 1011 (2020).
  • [19] Jang, L.-C., Kim, D.S., Kim, T., Lee, H. p-adic integral on Zp associated with degenerate Bernoulli polynomials of the second kind. Adv. Differ. Equ. 2020, 278 (2020).
  • [20] Jang, G.-W., Kim, T.: A note on type 2 degenerate Euler and Bernoulli polynomials. Adv. Stud. Contemp. Math. (Kyungshang). 29 (1), 147-159 (2019).
  • [21] Raza, N., Zainab, U., Araci, S., Esi, A.: Identities involving 3-variable Hermite polynomials arising from umbral method. Adv. Differ. Equ. 2020 (640), (2020).

Degenerate Poly-Type 2-Bernoulli Polynomials

Yıl 2021, Cilt: 9 Sayı: 1, 1 - 8, 01.03.2021
https://doi.org/10.36753/mathenot.839111

Öz

Recently, Kim-Kim [10] have studied type 2-Changhee and Daehee polynomials. They have also introduced the type 2-Bernoulli polynomials in order to express the central factorial numbers of the second kind by making use of type 2-Bernoulli numbers of negative integral orders. Inspired by their work, we consider a new class of generating functions of type 2-Bernoulli polynomials. We give some identities for these polynomials including type 2-Euler polynomials and Stirling numbers of the second kind.

Kaynakça

  • [1] Bayad, A., Hamahata, Y.: Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65, 15-24 (2012).
  • [2] Carlitz, L.: Degenerate Stirling, Bernoulli and Eulerian numbers. Utilitas Math. 15, 51-88 (1979).
  • [3] Chung, S.-K., Jang, G.-W., Kim, D.S., Kwon, J.: Some identities of the type 2 degenerate Bernoulli and Euler numbers. Adv. Stud. Contemp. Math. (Kyungshang). 29 (4), 613-632 (2019).
  • [4] Duran, U., Acikgoz, M., Araci, S.: Hermite based poly-Bernoulli polynomials with a q parameter, Adv. Stud. Contemp. Math. (Kyungshang). 28 (2), 285-296 (2018).
  • [5] Kaneko, M.: poly-Bernoulli numbers. J. Theor. Nombres Bordx. 9, 221-228 (1997).
  • [6] Kumar Sharma, S., Khan,W.A., Araci, S., Ahmed, S.S.: New type of degenerate Daehee polynomials of the second kind. Adv. Differ. Equ. 428 (2020).
  • [7] Sharma, S.K., Khan, W.A., Araci, S., Ahmed, S.S.: New construction of type 2 degenerate central Fubini polynomials with their certain properties. Adv. Differ. Equ. 587 (2020).
  • [8] Kilar, N., Simsek, Y.: Relations on Bernoulli and Euler polynomials related to trigonometric functions. Adv. Stud. Contemp. Math. (Kyungshang). 29 (2), 191-198 (2019).
  • [9] Kim, T., Kim, D.S., Kwon, J., Lee, H.: Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials. Adv. Differ. Equ. 168 (2020).
  • [10] Kim, T., Jang, Y.S; Seo, J.J: A note on Poly-Genocchi numbers and polynomials. Appl. Math. Sci. 8 (96), 4775-4781 (2014).
  • [11] Kim, T., Kim, D.S.: A note on type 2 Changhee and Daehee polynomials. RACSAM. 113, 2783-2791 (2019).
  • [12] Kim, D.S., Kim, T.: A note on degenerate poly-Bernoulli numbers and polynomials. Adv. Differ. Equ. 258 (2015).
  • [13] Kim, T., Kim, D.S., Kim, H.Y., Jang, L.-C.: Degenerate poly-Bernoulli numbers and polynomials. Informatica. 31 (3), 2-8 (2020).
  • [14] Kim, T., Jang, L.-C., Kim, D. S., Kim, H. Y.: Some identities on type 2 degenerate Bernoulli polynomials of the second kind. Symmetry. 12 (4), 510 (2020).
  • [15] Kim, D.S., Kim, T., Ryoo, C.S.: Generalized type 2 degenerate Euler numbers. Adv. Stud.Contemp. Math. (Kyungshang). 30 (2), 165-169, (2020).
  • [16] Kwon, J., Kim,W.J., Rim, S.-H.: On the some identities of the type 2 Daehee and Changhee polynomials arising from p-adic integrals on Zp. Proc. Jangjeon Math. Soc. 22 (3), 487-497 (2019).
  • [17] Kwon, J., Jang, L.-C.: A note on type 2 poly-Apostol-Bernoulli polynomials. Adv. Stud. Contemp. Math. (Kyungshang). 30 (2), 253-262 (2020).
  • [18] Lee, D.S., Kim, H.K., Jang, L.-C.: Type 2 degenerate poly-Euler Polynomials. Symmetry. 12, 1011 (2020).
  • [19] Jang, L.-C., Kim, D.S., Kim, T., Lee, H. p-adic integral on Zp associated with degenerate Bernoulli polynomials of the second kind. Adv. Differ. Equ. 2020, 278 (2020).
  • [20] Jang, G.-W., Kim, T.: A note on type 2 degenerate Euler and Bernoulli polynomials. Adv. Stud. Contemp. Math. (Kyungshang). 29 (1), 147-159 (2019).
  • [21] Raza, N., Zainab, U., Araci, S., Esi, A.: Identities involving 3-variable Hermite polynomials arising from umbral method. Adv. Differ. Equ. 2020 (640), (2020).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Serkan Araci 0000-0002-3950-6864

Yayımlanma Tarihi 1 Mart 2021
Gönderilme Tarihi 11 Aralık 2020
Kabul Tarihi 13 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Araci, S. (2021). Degenerate Poly-Type 2-Bernoulli Polynomials. Mathematical Sciences and Applications E-Notes, 9(1), 1-8. https://doi.org/10.36753/mathenot.839111
AMA Araci S. Degenerate Poly-Type 2-Bernoulli Polynomials. Math. Sci. Appl. E-Notes. Mart 2021;9(1):1-8. doi:10.36753/mathenot.839111
Chicago Araci, Serkan. “Degenerate Poly-Type 2-Bernoulli Polynomials”. Mathematical Sciences and Applications E-Notes 9, sy. 1 (Mart 2021): 1-8. https://doi.org/10.36753/mathenot.839111.
EndNote Araci S (01 Mart 2021) Degenerate Poly-Type 2-Bernoulli Polynomials. Mathematical Sciences and Applications E-Notes 9 1 1–8.
IEEE S. Araci, “Degenerate Poly-Type 2-Bernoulli Polynomials”, Math. Sci. Appl. E-Notes, c. 9, sy. 1, ss. 1–8, 2021, doi: 10.36753/mathenot.839111.
ISNAD Araci, Serkan. “Degenerate Poly-Type 2-Bernoulli Polynomials”. Mathematical Sciences and Applications E-Notes 9/1 (Mart 2021), 1-8. https://doi.org/10.36753/mathenot.839111.
JAMA Araci S. Degenerate Poly-Type 2-Bernoulli Polynomials. Math. Sci. Appl. E-Notes. 2021;9:1–8.
MLA Araci, Serkan. “Degenerate Poly-Type 2-Bernoulli Polynomials”. Mathematical Sciences and Applications E-Notes, c. 9, sy. 1, 2021, ss. 1-8, doi:10.36753/mathenot.839111.
Vancouver Araci S. Degenerate Poly-Type 2-Bernoulli Polynomials. Math. Sci. Appl. E-Notes. 2021;9(1):1-8.

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