SYMMETRIC IDENTITIES OF HIGHER-ORDER DEGENERATE q-BERNOULLI POLYNOMIALS

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참고문헌 (24)

1. A. Adelberg, "A nite difference approach to degenerate Bernoulli and Stirling polynomials", Discrete Math, 140(1-3), pp.1~21 (1995)
2. L. Carlitz, "q-Bernoulli and Eulerian numbers", Trans. Amer. Math. Soc, 76, pp.332~350 (1954)
3. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
4. Dmitry V. Dolgy, "SYMMETRIC IDENTITIES OF DEGENERATE q-BERNOULLI POLYNOMIALS UNDER SYMMETRY GROUP S3", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 19(1), pp.1~9 (2016), 장전수학회
5. Y. He, "Symmetric identities for Carlitz's q-Bernoulli numbers and polynomials", Adv. Difference Equ, pp.246~ (2013)
6. F. T. Howard, "Explicit formulas for degenerate Bernoulli numbers", Discrete Math, 162(1-3), pp.175~185 (1996)
7. 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (I)", Advanced Studies in Contemporary Mathematics, 23(3), pp.459~479 (2013), 장전수학회
8. 김대산, "Identities of symmetry for higher-order Euler polynomials in three variables (I)", Advanced Studies in Contemporary Mathematics, 22(1), pp.51~74 (2012), 장전수학회
9. 김대산, "Symmetry identities for generalized twisted Euler polynomials twisted by unramified roots of unity", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 15(3), pp.303~316 (2012), 장전수학회
10. D. S. Kim, "Some identities of symmetry for q-Bernoulli polynomials under sym-metric group of degree n", Ars Comb, 126, pp.435~441 (2016)
11. D. S. Kim, "Barnes-type Boole polynomials", Contrib. Discrete Math, 11(1), pp.7~15 (2016)
12. 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (II)", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(3), pp.359~378 (2013), 장전수학회
13. T. Kim, "q-Volkenborn integration", Russ. J. Math. Phys, 9(3), pp.288~299 (2002)
14. T. Kim, "Identities involving degenerate Euler numbers and polynomials arising from non-linear differential equations", J. Nonlinear Sci. Appl, 9(5), pp.2086~2098 (2016)
15. 김태균, "Identities of symmetry for (h,q)-extensions of generalized higher-order Euler polynomials", Advanced Studies in Contemporary Mathematics, 26(3), pp.579~585 (2016), 장전수학회
16. 김태균, "Revisit nonlinear differential equations arising from the generating functions of degenerate Bernoulli numbers", Advanced Studies in Contemporary Mathematics, 26(3), pp.401~406 (2016), 장전수학회
17. 김태균, "On degenerate $q$-Bernoulli polynomials", 대한수학회보, 53(4), pp.1149~1156 (2016), 대한수학회
18. T. Kim, "Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on Zp", Russ. J. Math. Phys, 16(1), pp.93~96 (2009)
19. 김영희, "Symmetry of power sum and twisted Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 18(2), pp.127~133 (2009), 장전수학회
20. G. D. Liu, "Degenerate Bernoulli numbers and polynomials of higher order", (Chinese), J. Math. (Wuhan), 25(3), pp.283~288 (2005)
21. E. -J. Moon, "On the symmetric properties of higher-order twisted q-Euler numbers polynomials", Adv. Difference Equ, pp.8~ (2010)
22. 유천성, "A note on the weighted q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 21(1), pp.47~54 (2011), 장전수학회
23. H. M. Srivastava, "q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and bases L-series", Russ. J. Math. Phys, 12(2,), pp.241~268 (2005)
24. Z. Zhang, "On sums of products of the degenerate Bernoulli numbers", Integral Transforms Spec. Funct, 20(9-10), pp.751~755 (2009)

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