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Year 2021, Volume: 9 Issue: 2, 337 - 341, 15.10.2021

Abstract

References

  • [1] S. Araci, E. Agyüz, M. Acikgoz, On a q-analog of some numbers and polynomials, J. Inequal. Appl., 19, 2015 doi:10.1186/s13660-014-0542-y.
  • [2] Y.K. Cho, T. Kim, T. Mansour, S.-H. Rim, Higher order q-Daehee polynomials, J. Comput. Anal. Appl., 19 (1), 2015,167-173.
  • [3] J. Diamond, The p-adic log gamma function and p-adic Euler constant, Trans. Amer. Math. Soc., 233, 1977, 321-337.
  • [4] U. Duran, M. Acikgoz, On p-adic gamma function related to q-Daehee polynomials and numbers, accepted for publicationin Proyecciones J. Math., 2018.
  • [5] B. N. Guo, F. Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, Anal. Appl., 19 (1), 2015,167-173.
  • [6] Ö. Ç. Havara and H. Menken, On the Volkenborn integral of the q-extension of the p-adic gamma function, J. Math. Anal.,8 (2), 2017, 64-72.
  • [7] Ö. Ç. Havare and H. Menken, The Volkenborn integral of the p-adic gamma function, Int. J. Adv. Appl. Funct., 5 (2),2018, 56-59.
  • [8] Y. S. Kim, q-analogues of p-adic gamma functions and p-adic Euler constants, Comm. Korean Math. Soc., 13 (4), 1998,735–741.
  • [9] T. Kim, S.-H. Lee, T. Mansour and J.-J. Seo, A note on q-Daehee polynomials and numbers, Adv. Stud. Contemp. Math.,24 (2), 2014, 155-160.
  • [10] D. S. Kim and T. Kim, Daehee numbers and polynomials, Appl. Math. Sci., 7 (120), 2013, 5969-5976.
  • [11] N. Koblitz, p-adic numbers, p-adic analysis, and Zeta functions (Springer-Verlag, New York Inc, 1977).
  • [12] K. Mahler, An interpolation series for continuous functions of a p-adic variable, J. Reine Angew. Math., 199, 1958, 23-34.
  • [13] H. Menken, A. Körükçü, Some properties of the q-extension of the p-adic gamma function, Abst. Appl. Anal., Volume2013, Article ID 176470, 4 pages.
  • [14] Y. Morita, A p-adic analogue of the gamma-function, J. Fac. Sci., 22 (2), 1975, 255-266.
  • [15] H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp.Math., 18 (1), 2009, 41-48.
  • [16] A. M. Robert, A course in p-adic analysis (Springer-Verlag New York, Inc., 2000).
  • [17] Y. Simsek, Apostol type Daehee numbers and polynomials, Adv. Stud. Contemp. Math.,

Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials

Year 2021, Volume: 9 Issue: 2, 337 - 341, 15.10.2021

Abstract

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

References

  • [1] S. Araci, E. Agyüz, M. Acikgoz, On a q-analog of some numbers and polynomials, J. Inequal. Appl., 19, 2015 doi:10.1186/s13660-014-0542-y.
  • [2] Y.K. Cho, T. Kim, T. Mansour, S.-H. Rim, Higher order q-Daehee polynomials, J. Comput. Anal. Appl., 19 (1), 2015,167-173.
  • [3] J. Diamond, The p-adic log gamma function and p-adic Euler constant, Trans. Amer. Math. Soc., 233, 1977, 321-337.
  • [4] U. Duran, M. Acikgoz, On p-adic gamma function related to q-Daehee polynomials and numbers, accepted for publicationin Proyecciones J. Math., 2018.
  • [5] B. N. Guo, F. Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, Anal. Appl., 19 (1), 2015,167-173.
  • [6] Ö. Ç. Havara and H. Menken, On the Volkenborn integral of the q-extension of the p-adic gamma function, J. Math. Anal.,8 (2), 2017, 64-72.
  • [7] Ö. Ç. Havare and H. Menken, The Volkenborn integral of the p-adic gamma function, Int. J. Adv. Appl. Funct., 5 (2),2018, 56-59.
  • [8] Y. S. Kim, q-analogues of p-adic gamma functions and p-adic Euler constants, Comm. Korean Math. Soc., 13 (4), 1998,735–741.
  • [9] T. Kim, S.-H. Lee, T. Mansour and J.-J. Seo, A note on q-Daehee polynomials and numbers, Adv. Stud. Contemp. Math.,24 (2), 2014, 155-160.
  • [10] D. S. Kim and T. Kim, Daehee numbers and polynomials, Appl. Math. Sci., 7 (120), 2013, 5969-5976.
  • [11] N. Koblitz, p-adic numbers, p-adic analysis, and Zeta functions (Springer-Verlag, New York Inc, 1977).
  • [12] K. Mahler, An interpolation series for continuous functions of a p-adic variable, J. Reine Angew. Math., 199, 1958, 23-34.
  • [13] H. Menken, A. Körükçü, Some properties of the q-extension of the p-adic gamma function, Abst. Appl. Anal., Volume2013, Article ID 176470, 4 pages.
  • [14] Y. Morita, A p-adic analogue of the gamma-function, J. Fac. Sci., 22 (2), 1975, 255-266.
  • [15] H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp.Math., 18 (1), 2009, 41-48.
  • [16] A. M. Robert, A course in p-adic analysis (Springer-Verlag New York, Inc., 2000).
  • [17] Y. Simsek, Apostol type Daehee numbers and polynomials, Adv. Stud. Contemp. Math.,
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ugur Duran 0000-0002-5717-1199

Mehmet Acikgoz 0000-0003-1091-9697

Publication Date October 15, 2021
Submission Date June 10, 2019
Acceptance Date May 25, 2021
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Duran, U., & Acikgoz, M. (2021). Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials. Konuralp Journal of Mathematics, 9(2), 337-341.
AMA Duran U, Acikgoz M. Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials. Konuralp J. Math. October 2021;9(2):337-341.
Chicago Duran, Ugur, and Mehmet Acikgoz. “Relationships Between Mahler Expansion and Higher Order Q-Daehee Polynomials”. Konuralp Journal of Mathematics 9, no. 2 (October 2021): 337-41.
EndNote Duran U, Acikgoz M (October 1, 2021) Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials. Konuralp Journal of Mathematics 9 2 337–341.
IEEE U. Duran and M. Acikgoz, “Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials”, Konuralp J. Math., vol. 9, no. 2, pp. 337–341, 2021.
ISNAD Duran, Ugur - Acikgoz, Mehmet. “Relationships Between Mahler Expansion and Higher Order Q-Daehee Polynomials”. Konuralp Journal of Mathematics 9/2 (October 2021), 337-341.
JAMA Duran U, Acikgoz M. Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials. Konuralp J. Math. 2021;9:337–341.
MLA Duran, Ugur and Mehmet Acikgoz. “Relationships Between Mahler Expansion and Higher Order Q-Daehee Polynomials”. Konuralp Journal of Mathematics, vol. 9, no. 2, 2021, pp. 337-41.
Vancouver Duran U, Acikgoz M. Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials. Konuralp J. Math. 2021;9(2):337-41.
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