A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function
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Authors
C. K. An
- Department of Mathematics, Hannam University, Daejeon 306-791, Korea.
H. Y. Lee
- Department of Mathematics, Hannam University, Daejeon 306-791, Korea.
Y. R. Kim
- Department of Mathematics, Hannam University, Daejeon 306-791, Korea.
Abstract
In this paper we consider a new type of the \(q\)-Apostol Bernoulli numbers and polynomials. Firstly, we define the \(q\)-Apostol Bernoulli numbers and polynomials by making use of their generating function. Also, we observe many properties, i.e., the recurrence formula, the difference equation, the differential relation.
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ISRP Style
C. K. An, H. Y. Lee, Y. R. Kim, A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 1, 56--64
AMA Style
An C. K., Lee H. Y., Kim Y. R., A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function. J. Nonlinear Sci. Appl. (2019); 12(1):56--64
Chicago/Turabian Style
An, C. K., Lee, H. Y., Kim, Y. R.. "A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function." Journal of Nonlinear Sciences and Applications, 12, no. 1 (2019): 56--64
Keywords
- The second kind \(q\)-Apostol Bernoulli polynomials
- the second kind \(q\)-Apostol Bernoulli numbers
- zeta function
MSC
References
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