On \((h,q)\) -Daehee numbers and polynomials

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• 作者：Younghae Do (1)
  Dongkyu Lim (1)
  
  1. Department of Mathematics ; Kyungpook National University ; Daegu ; 702-701 ; S. Korea
  
• 关键词：11B68 ; 11S40 ; ( h ; q ) $(h ; q)$ ; Daehee numbers ; ( h ; q ) $(h ; q)$ ; Daehee polynomials ; ( h ; q ) $(h ; q)$ ; Bernoulli polynomials ; p ; adic q ; integral
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：986 KB
• 参考文献：1. Kim, T (2002) q-Volkenborn integration. Russ. J. Math. Phys. 9: pp. 288-299
  2. Kim, T (2008) q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients. Russ. J. Math. Phys. 15: pp. 51-57 CrossRef
  3. Kim, T, Lee, S-H, Mansour, T, Seo, J-J (2014) A note on q-Daehee polynomials and numbers. Adv. Stud. Contemp. Math. 24: pp. 155-160
  4. Lim, D: Modified / q-Daehee numbers and polynomials. J. Comput. Anal. Appl. (2015, submitted)
  5. Kwon, J, Park, J-W, Pyo, S-S, Rim, S-H (2013) A note on the modified q-Euler polynomials. JP J. Algebra Number Theory Appl. 31: pp. 107-117
  6. Moon, E-J, Park, J-W, Rim, S-H (2014) A note on the generalized q-Daehee numbers of higher order. Proc. Jangjeon Math. Soc. 17: pp. 557-565
  7. Ozden, H, Cangul, IN, Simsek, Y (2009) Remarks on q-Bernoulli numbers associated with Daehee numbers. Adv. Stud. Contemp. Math. (Kyungshang) 18: pp. 41-48
  8. Park, J-W (2014) On the twisted Daehee polynomials with q-parameter. Adv. Differ. Equ. 2014: CrossRef
  9. Park, J-W, Rim, S-H, Kwon, J (2014) The twisted Daehee numbers and polynomials. Adv. Differ. Equ. 2014: CrossRef
  10. Ryoo, CS (2010) A note on the ( h , q ) $(h,q)$ -Bernoulli polynomials. Far East J. Math. Sci. 41: pp. 45-53
  11. Ryoo, CS, Kim, T (2011) A new identities on the q-Bernoulli numbers and polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 21: pp. 161-169
  12. Seo, JJ, Rim, S-H, Kim, T, Lee, SH (2014) Sums products of generalized Daehee numbers. Proc. Jangjeon Math. Soc. 17: pp. 1-9
  13. Simsek, Y (2006) Twisted ( h , q ) $(h,q)$ -Bernoulli numbers and polynomials related to twisted ( h , q ) $(h,q)$ -zeta function and L-function. J.聽Math. Anal. Appl. 324: pp. 790-804 CrossRef
  14. Simsek, Y (2007) The behavior of the twisted p-adic ( h , q ) $(h,q)$ -L-functions at s = 0 $s=0$. J. Korean Math. Soc. 44: pp. 915-929 CrossRef
  15. Simsek, Y, Rim, S-H, Jang, L-C, Kang, D-J, Seo, J-J (2005) A note on q-Daehee sums. J. Anal. Comput. 1: pp. 151-160
  16. Srivastava, HM, Kim, T, Jang, L-C, Simsek, Y (2005) q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series. Russ. J. Math. Phys. 12: pp. 241-268
  17. Araci, S, Acikgoz, M, Esi, A (2012) A note on the q-Dedekind-type Daehee-Changhee sums with weight 伪 arising from modified q-Genocchi polynomials with weight 伪. J. Assam Acad. Math. 5: pp. 47-54
  18. Bayad, A (2010) Modular properties of elliptic Bernoulli and Euler functions. Adv. Stud. Contemp. Math. (Kyungshang) 20: pp. 389-401
  19. Dolgy, DV, Kim, T, Rim, S-H, Lee, SH (2014) Symmetry identities for the generalized higher-order q-Bernoulli polynomials under S 3 $S_{3}$ arising from p-adic Volkenborn integral on Z p $\Bbb{Z}_{p}$. Proc. Jangjeon Math. Soc. 17: pp. 645-650
  20. Kim, DS, Kim, T (2013) Daehee numbers and polynomials. Appl. Math. Sci. (Ruse) 7: pp. 5969-5976
  21. Kim, DS, Kim, T (2014) q-Bernoulli polynomials and q-umbral calculus. Sci. China Math. 57: pp. 1867-1874 CrossRef
  22. Kim, DS, Kim, T, Komatsu, T, Lee, S-H (2014) Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials. Adv. Differ. Equ. 2014: CrossRef
  23. Kim, DS, Kim, T, Lee, S-H, Seo, J-J (2014) Higher-order Daehee numbers and polynomials. Int. J. Math. Anal. 8: pp. 273-283
  24. Kim, DS, Kim, T, Seo, J-J (2014) Higher-order Daehee polynomials of the first kind with umbral calculus. Adv. Stud. Contemp. Math. (Kyungshang) 24: pp. 5-18
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

The p-adic q-integral (sometimes called q-Volkenborn integration) was defined by Kim. From p-adic q-integral equations, we can derive various q-extensions of Bernoulli polynomials and numbers. DS Kim and T Kim studied Daehee polynomials and numbers and their applications. Kim et al. introduced the q-analogue of Daehee numbers and polynomials which are called q-Daehee numbers and polynomials. Lim considered the modified q-Daehee numbers and polynomials which are different from the q-Daehee numbers and polynomials of Kim et al. In this paper, we consider \((h,q)\) -Daehee numbers and polynomials and give some interesting identities. In case \(h=0\) , we cover the q-analogue of Daehee numbers and polynomials of Kim et al. In case \(h=1\) , we modify q-Daehee numbers and polynomials. We can find out various \((h,q)\) -related numbers and polynomials which are studied by many authors.