Fourier series of functions associated with higher-order Bernoulli polynomials
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Authors
Taekyun Kim
- Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300160, China.
- Department of Mathematics, College of Natural Science, Kwangwoon University, Seoul 139-701, Republic of Korea.
Dae San Kim
- Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea.
Dmitry V. Dolgy
- Hrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea.
Jin-Woo Park
- Department of Mathematics Education, Daegu University, Gyeongsan-si, Gyeongsangbuk-do, 712-714, Republic of Korea.
Abstract
In this paper, we consider three types of functions associated with higher-order Bernoulli polynomials and derive their
Fourier series expansions. Further, we express each of them in term of Bernoulli functions.
Share and Cite
ISRP Style
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Jin-Woo Park, Fourier series of functions associated with higher-order Bernoulli polynomials, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2579--2591
AMA Style
Kim Taekyun, Kim Dae San, Dolgy Dmitry V., Park Jin-Woo, Fourier series of functions associated with higher-order Bernoulli polynomials. J. Nonlinear Sci. Appl. (2017); 10(5):2579--2591
Chicago/Turabian Style
Kim, Taekyun, Kim, Dae San, Dolgy, Dmitry V., Park, Jin-Woo. "Fourier series of functions associated with higher-order Bernoulli polynomials." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2579--2591
Keywords
- Fourier series
- higher-order Bernoulli polynomials
- Bernoulli functions.
MSC
References
-
[1]
M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, For sale by the Superintendent of Documents, U.S. Government Printing Office,, Washington, D.C. (1964)
-
[2]
L. Carlitz, A note on Bernoulli numbers and polynomials, Elem. Math., 29 (1974), 90–92.
-
[3]
G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225–249.
-
[4]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173–199.
-
[5]
I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory, 110 (2005), 75–82.
-
[6]
H. W. Gould, Explicit formulas for Bernoulli numbers, Amer. Math. Monthly, 79 (1972), 44–51.
-
[7]
D. S. Kim, T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 12 pages.
-
[8]
D. S. Kim, T. Kim, A note on higher-order Bernoulli polynomials, J. Inequal. Appl., 2013 (2013), 9 pages.
-
[9]
D. S. Kim, T. Kim, Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct., 24 (2013), 734–738.
-
[10]
D. S. Kim, T. Kim, Higher-order Bernoulli and poly-Bernoulli mixed type polynomials, Georgian Math. J., 22 (2015), 265–272.
-
[11]
D. S. Kim, T. Kim, Fourier series of higher-order Euler functions and their applications, Bull. Korean Math. Soc., (to appear),
-
[12]
D. S. Kim, T. Kim, Y. H. Kim, S.-H. Lee , Some arithmetic properties of Bernoulli and Euler numbers, Adv. Stud. Contemp. Math. (Kyungshang), 22 (2012), 467–480.
-
[13]
T. Kim, D. S. Kim, S.-H. Rim, D. V. Dolgy, Fourier series of higher-order Bernoulli functions and their applications, J. Inequal. Appl., 2017 (2017), 7 pages.
-
[14]
D. H. Lehmer, A new approach to Bernoulli polynomials, Amer. Math. Monthly, 95 (1988), 905–911.
-
[15]
J. E. Marsden, Elementary classical analysis, With the assistance of Michael Buchner, Amy Erickson, Adam Hausknecht, Dennis Heifetz, Janet Macrae and William Wilson, and with contributions by Paul Chernoff, István Fáry and Robert Gulliver, W. H. Freeman and Co., San Francisco (1974)
-
[16]
K. Shiratani, S. Yokoyama , An application of p-adic convolutions, Mem. Fac. Sci. Kyushu Univ. Ser. A, 36 (1982), 73–83.
-
[17]
L. C. Washington, Introduction to cyclotomic fields, Second edition, Graduate Texts in Mathematics, Springer-Verlag, New York (1997)
-
[18]
D. G. Zill, M. R. Cullen, Advanced engineering mathematics, Second edition, Jones and Bartlett Publishers, London, UK (2000)