Acknowledgement
The corresponding author is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT). (No. 2021R1F1A1051093)
References
- S.D. Kim and M-S. Kim, New identities involving Bernoulli, Euler and Genocchi numbers, Adv. Difference Equ. 2013:74 (2013), 15 pp.
- N.S. Jung and C.S. Ryoo, A reserach on a new apporach to Euler polynomials and Bernstein polynomials with variable [x]q, J. Appl. Math. & Informatics 35 (2017), 205-215. https://doi.org/10.14317/JAMI.2017.205
- D. Kim, A. Kim and N.Y. Ikikardes, Bernoulli numbers and certain convolution sums with divisor functions, Adv. Difference Equ. 2013:277 (2013), 20pp.
- M-S. Kim, Generalized Euler power series, J. Appl. Math. & Informatics 38 (2020), 591-600. https://doi.org/10.14317/JAMI.2020.591
- M.B. Nathanson, Additive Number Theory, The Classical Bases, Graduate Texts in Mathematics 164, Springer, 1996.
- S. Ramanujan, On Certain Trigonometric Sums and their Applications in the Theory of Numbers, Transactions of the Cambridge Philosophical Society XXII 13 (1918), 259-276.
- Z. Sun, Introduction to Bernoulli and Euler polynomials, http://maths.nju.edu.cn/~zwsun/BerE.pdf.
- K.S. Williams, Number Theory in the Spirit of Liouville, Cambridge University Press, New York, 2011.