A Note on a New Type of Degenerate Bernoulli Numbers

Russian Journal of Mathematical Physics - Tập 27 Số 2 - Trang 227-235 - 2020
D. S. Kim1, T. Kim2
1Department of Mathematics, Sogang University, Seoul, Republic of Korea
2Department of Mathematics, Kwangwoon University, Seoul, Republic of Korea

Tóm tắt

Từ khóa


Tài liệu tham khảo

L. Carlitz, “Degenerate Stirling, Bernoulli and Eulerian Numbers,” Util. Math. 15, 51–88 (1979).

L. Carlitz, “A Degenerate Staudt-Clausen Theorem,” Arch. Math. (Basel) 7, 28–33 (1956).

D. V. Dolgy and T. Kim, “Some Explicit Formulas of Degenerate Stirling Numbers Associated with the Degenerate Special Numbers and Polynomials,” Proc. Jangjeon Math. Soc. 21 (2), 309–317 (2018).

D. V. Dolgy, T. Kim, H.-I. Kwon, and J. J. Seo, “Some Identities for Degenerate Euler Numbers and Polynomials Arising from Degenerate Bell Polynomials,” Proc. Jangjeon Math. Soc. 19 (3), 457–464 (2016).

Y. He and W. Zhang, “A Three-Term Reciprocity Formula for Bernoulli Polynomials,” Util. Math. 100, 23–31 (2016).

W. A. Khan, “A Note on Degenerate Hermite Poly-Bernoulli Numbers and Polynomials,” J. Class. Anal. 8, 65–76 (2016).

W. A. Khan, “A New Class of Degenerate Frobenius-Euler-Hermite Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 28 (4), 567–576 (2018).

J. Jeong and S.-H. Rim, “On Finite Times Degenerate Higher-Order Cauchy Numbers and Polynomials,” Bull. Korean Math. Soc. 53 (5), 1427–1437 (2016).

D. S. Kim and T. Kim, “Some Applications of Degenerate Poly-Bernoulli Numbers and Polynomials,” Georgian Math. J. 26 (3), 415–421 (2019).

D. S. Kim and T. Kim, “A Note on Polyexponential and Unipoly Functions,” Russ. J. Math. Phys. 26 (1), 40–49 (2019).

T. Kim, “A Note on Degenerate Stirling Polynomials of the Second Kind,” Proc. Jangjeon Math. Soc. 20 (3), 319–331 (2017).

T. Kim, “λ-Analogue of Stirling Numbers of the First Kind,” Adv. Stud. Contemp. Math. (Kyungshang) 27 (3), 423–429 (2017).

T. Kim, D. S. Kim, L.-C. Jang, and H.-Y. Kim, “On Type 2 Degenerate Bernoulli and Euler Polynomials of Complex Variable,” Adv. Difference Equ. 2019 (490), pp. 15.

T. Kim and D. S. Kim, “Identities for Degenerate Bernoulli Polynomials and Korobov Polynomials of the First Kind,” Sci. China Math. 62 (5), 999–1028 (2019).

T. Kim, D. S. Kim, and H.-I. Kwon, “Some Identities of Carlitz Degenerate Bernoulli Numbers and Polynomials,” Iran. J. Sci. Technol. Trans. A Sci. 41 (3), 749–753 (2017).

T. Kim and G.-W. Jang, “Higher-Order Degenerate q-Bernoulli Polynomials,” Proc. Jangjeon Math. Soc. 20 (1), 51–60 (2017).

T. Kim and D. S. Kim, “Degenerate Laplace Transform and Degenerate Gamma Function,” Russ. J. Math. Phys. 24 (2), 241–248 (2017).

T. Kim, Y. Yao, D. S. Kim, and G.-W. Jang, “Degenerate r-Stirling Numbers and r-Bell Polynomials,” Russ. J. Math. Phys. 25 (1), 44–58 (2018).

Y. Kim and J.-W. Park, “On the Degenerate (h, q)-Changhee Numbers and Polynomials,” J. Inequal. Appl. 2019 (5), pp. 15.

D. V. Kruchinin and V. V. Kruchinin, “Explicit Formula for Reciprocal Generating Function and Its Application,” Adv. Stud. Contemp. Math. (Kyungshang) 29 (3), 365–372 (2019).

D. Lim, “Modified Degenerate Daehee Numbers and Polynomials Arising from Differential Equations,” Adv. Stud. Contemp. Math. (Kyungshang) 28 (3), 497–506 (2019).

L. Lewin, “Polylogarithms and Associated Functions. With a Foreword by A. J. Van der Poorten,” North-Holland Publishing Co., New York-Amsterdam, 1981. xvii+359, ISBN: 0-444-00550-1.

J. Lee and J. Kwon, “The Modified Degenerate q-Bernoulli Polynomials Arising from p-Adic Invariant Integral on Zp,” Adv. Difference Equ. 2017 (29), pp. 9.

S. Roman, “The Umbral Calculus,” Pure Appl. Math., 111. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1984. x+193, ISBN: 0-12-594380-6.

Y. Simsek, “Identities on the Changhee Numbers and Apostol-Type Daehee Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 27 (2), 199–212 (2017).

M. Wu and S. S. Du, “A Symmetric Identity for Degenerate Higher-Order Bernoulli Polynomials and Generalized Power Sum Polynomials,” (Chinese) Math. Pract. Theory 44 (24), 256–261 (2014).