Fourier expansions for Genocchi polynomials of higher order
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Authors
Cristina B. Corcino
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines.
Baby Ann A. Damgo
- Mathematics Department, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines.
Roberto B. Corcino
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines.
Abstract
In this paper, Fourier expansions and integral representations for Genocchi polynomials of higher order are established. Using the Fourier expansion, the explicit formula for Genocchi polynomials at rational arguments in terms of Hurwitz zeta function is also obtained.
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ISRP Style
Cristina B. Corcino, Baby Ann A. Damgo, Roberto B. Corcino, Fourier expansions for Genocchi polynomials of higher order, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 59--72
AMA Style
Corcino Cristina B., Damgo Baby Ann A., Corcino Roberto B., Fourier expansions for Genocchi polynomials of higher order. J Math Comput SCI-JM. (2021); 22(1):59--72
Chicago/Turabian Style
Corcino, Cristina B., Damgo, Baby Ann A., Corcino, Roberto B.. "Fourier expansions for Genocchi polynomials of higher order." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 59--72
Keywords
- Genocchi polynomials
- Bernoulli polynomials
- Euler polynomials
- Fourier series
- Hurwitz zeta function
MSC
References
-
[1]
S. Araci, M. Acikgoz, Applications of Fourier Series and Zeta Functions to Genocchi Polynomials, Appl. Math. Inf. Sci., 12 (2018), 951--955
-
[2]
S. Araci, M. Acikgoz, Construction of Fourier expansion of Apostol Frobenius-Euler polynomials and its application, Adv. Difference Equ., 2018 (2018), 14 pages
-
[3]
S. Araci, E. Sen, M. Acikgoz, Theorems on Genocchi polynomials of higher order arising from Genocchi basis, Taiwanese J. Math., 18 (2014), 473--482
-
[4]
A. Bayad, Fourier expansions for Apostol-Bernoulli, Apostol- Euler and Apostol-Genocchi polynomials, Math Comp., 80 (2011), 2219--2221
-
[5]
R. V. Churchill, J. W. Brown, Complex variables and applications, McGraw-Hill, Boston (2009)
-
[6]
C. B. Corcino, R. B. Corcino, Asymptotics of Genocchi polynomials and higher order Genocchi polynomials using residues, Afr. Mat., 2020 (2020), 13 pages
-
[7]
A. F. Horadam, Genocchi Polynomials, In: Application of Fibonacci Numbers, 1991 (1991), 145--166
-
[8]
D. S. Kim, T. Kim, A Note on Higher-Order Bernoulli Polynomials, J. Inequal. Appl., 2013 (2013), 9 pages
-
[9]
M. Kir, H. Dutta, M. Acikgoz, S. Araci, Identities on Some Special Poynomials Derived from the Concepts of n-Normed Structures, Accretive Operators and Contraction Mappings, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018), 787--792
-
[10]
J. L. Lopez, N. M. Temme, Large degree asymptotics of generalized Bernoulli and Euler polynomials, J. Math. Anal. Appl., 363 (2010), 197--208
-
[11]
Q.-M Luo, Fourier expansion and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials, Math. Comp., 78 (2009), 2193--2208
-
[12]
Q.-M. Luo, Fourier expansions and integral representations for Genocchi polynomials, J. Integer Seq., 12 (2009), 9 pages
-
[13]
Q.-M. Luo, Extensions of the Genocchi Polynomials and their Fourier expansions and integral representations, Osaka J. Math., 48 (2011), 291--309
-
[14]
Q.-M. Luo, H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308 (2005), 390--302
-
[15]
Q.-M. Luo, H. M. Srivastava, Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput., 217 (2011), 5702--5728
-
[16]
R. Niu, Fourier Series and Their Applications, Technical Reports (MIT), 2006 (2006), 13 pages