Some identities of degenerate special polynomials

Dae San Kim; Taekyun Kim

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 295-302
  • ISSN: 2391-5455

Abstract

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In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.

How to cite

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Dae San Kim, and Taekyun Kim. "Some identities of degenerate special polynomials." Open Mathematics 13.1 (2015): 295-302. <http://eudml.org/doc/270961>.

@article{DaeSanKim2015,
abstract = {In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.},
author = {Dae San Kim, Taekyun Kim},
journal = {Open Mathematics},
keywords = {Mixed-type degenerate special polynomial; Fermionic integral; Bosonic integral; degenerate Euler polynomial; fermionic -adic integral},
language = {eng},
number = {1},
pages = {295-302},
title = {Some identities of degenerate special polynomials},
url = {http://eudml.org/doc/270961},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Dae San Kim
AU - Taekyun Kim
TI - Some identities of degenerate special polynomials
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 295
EP - 302
AB - In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.
LA - eng
KW - Mixed-type degenerate special polynomial; Fermionic integral; Bosonic integral; degenerate Euler polynomial; fermionic -adic integral
UR - http://eudml.org/doc/270961
ER -

References

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  1. [1] Araci, S., Acikgoz, M., A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials., Adv. Stud. Contemp. Math. (Kyungshang), 2012, 22(3), 399–406. Zbl1261.05003
  2. [2] Bayad A., Chikhi J., Apostol-Euler polynomials and asymptotics for negative binomial reciprocals., Adv. Stud. Contemp. Math. (Kyungshang), 2014, 24(1), 33–37. Zbl1317.11026
  3. [3] Carlitz L., Degenerate Stirling, Bernoulli and Eulerian numbers., Utilitas Math., 1979, 15, 51–88. 
  4. [4] Ding D., Yang J., Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials., Adv. Stud. Contemp. Math. (Kyungshang), 2010, 20(1), 7–21. Zbl1192.05001
  5. [5] Gaboury S., Tremblay R., Fugère B.-J., Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials., Proc. Jangjeon Math. Soc., 2014, 17(1), 115–123. Zbl06315773
  6. [6] He Y., Zhang W., A convolution formula for Bernoulli polynomials., Ars Combin., 2013, 108, 97–104. Zbl1289.11017
  7. [7] Jeong J.-H., Jin J.-H., Park J.-W., Rim S.-H., On the twisted weak q-Euler numbers and polynomials with weight 0., Proc. Jangjeon Math. Soc., 2013, 16(2), 157–163. Zbl1297.11010
  8. [8] Jolany H., and Darafsheh M. R., Some other remarks on the generalization of Bernoulli and Euler numbers., Sci. Magna, 2009, 5(3), 118–129. Zbl1296.11013
  9. [9] Kim D. S., and Kim T., Higher-order Degenerate Euler Polynomials., Applied Mathematical Sciences, 2015, 9(2), 57–73. 
  10. [10] Kim D. S., Kim T., Komatsu T., and Lee S.-H., Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials., Adv. Difference Equ., 2014, 2014:140, pp 22. 
  11. [11] Kim T., q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients., Russ. J. Math. Phys., 2008, 15(1), 51–57. [WoS] Zbl1196.11040
  12. [12] Kim T., Symmetry p-adic invariant integral on Zp for Bernoulli and Euler polynomials., J. Difference Equ. Appl., 2008, 14(12), 1267–1277. Zbl1229.11152
  13. [13] Kim T., Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on Zp., Russ. J. Math. Phys., 2009, 16(1), 93–96. [WoS] Zbl1200.11089
  14. [14] Luo Q.-M., Qi F., Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials., Adv. Stud. Contemp. Math. (Kyungshang), 2013, 7(1), 11–18. Zbl1042.11012
  15. [15] Ozden H., q-Dirichlet type L-functions with weight α., Adv. Difference Equ., 2013, 2013:40, pp 5. 
  16. [16] Ozden H., Cangul, I. N., Simsek Y., Remarks on q-Bernoulli numbers associated with Daehee numbers., Adv. Stud. Contemp. Math. (Kyungshang), 2009, 18(1), 41–48. Zbl1188.05005
  17. [17] Park J.-W., New approach to q-Bernoulli polynomials with weight or weak weight., Adv. Stud. Contemp. Math. (Kyungshang), 2014, 24(1), 39–44. Zbl1317.11028
  18. [18] Roman, S., The umbral calculus, vol. 111 of Pure and Applied Mathematics., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1984. 
  19. [19] Ryoo C. S., Song H., and Agarwal R. P., On the roots of the q-analogue of Euler-Barnes’ polynomials., Adv. Stud. Contemp. Math. (Kyungshang), 2004, 9(2), 153–163. Zbl1068.11013
  20. [20] S¸ en E., Theorems on Apostol-Euler polynomials of higher order arising from Euler basis., Adv. Stud. Contemp. Math. (Kyungshang), 2013, 23(2), 337–345. Zbl1297.11008
  21. [21] Simsek Y., Interpolation functions of the Eulerian type polynomials and numbers., Adv. Stud. Contemp. Math. (Kyungshang), 2013, 23(2), 301–307. Zbl06280544
  22. [22] Volkenborn A., Ein P-adisches Integral und seine Anwendungen. I., Manuscripta Math., 1972, 7, 341–373. [Crossref] Zbl0245.10045
  23. [23] Volkenborn A., Ein p-adisches Integral und seine Anwendungen. II., Manuscripta Math. 1974, 12, 17–46. [Crossref] Zbl0276.12018
  24. [24] Zhang Z., and Yang H., Some closed formulas for generalized Bernoulli-Euler numbers and polynomials., Proc. Jangjeon Math. Soc., 2008, 11(2), 191–198. Zbl1178.05003

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