Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function
Апстракт
It is shown that there exists a companion formula to Srivastavas formula for the Lipschitz-Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner. (C) 2009 Elsevier Ltd. All rights reserved.
Кључне речи:
Hurwitz-Lerch Zeta function / Lipschitz-Lerch Zeta function / Lerch Zeta function / Hurwitz Zeta function / Riemann Zeta function / Legendre chi function / Bernoulli polynomials / Bernoulli numbers / Discrete Fourier transformИзвор:
Applied Mathematics Letters, 2009, 22, 7, 1081-1084Финансирање / пројекти:
- Ministry of Science of the Republic of Serbia [144004], Natural Sciences and Engineering Research Council of Canada [OGP0007353]
DOI: 10.1016/j.aml.2008.08.024
ISSN: 0893-9659
WoS: 000266894100022
Scopus: 2-s2.0-67349287402
Колекције
Институција/група
VinčaTY - JOUR AU - Cvijović, Đurđe AU - Srivastava, H. M. PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3721 AB - It is shown that there exists a companion formula to Srivastavas formula for the Lipschitz-Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner. (C) 2009 Elsevier Ltd. All rights reserved. T2 - Applied Mathematics Letters T1 - Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function VL - 22 IS - 7 SP - 1081 EP - 1084 DO - 10.1016/j.aml.2008.08.024 ER -
@article{ author = "Cvijović, Đurđe and Srivastava, H. M.", year = "2009", abstract = "It is shown that there exists a companion formula to Srivastavas formula for the Lipschitz-Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner. (C) 2009 Elsevier Ltd. All rights reserved.", journal = "Applied Mathematics Letters", title = "Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function", volume = "22", number = "7", pages = "1081-1084", doi = "10.1016/j.aml.2008.08.024" }
Cvijović, Đ.,& Srivastava, H. M.. (2009). Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function. in Applied Mathematics Letters, 22(7), 1081-1084. https://doi.org/10.1016/j.aml.2008.08.024
Cvijović Đ, Srivastava HM. Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function. in Applied Mathematics Letters. 2009;22(7):1081-1084. doi:10.1016/j.aml.2008.08.024 .
Cvijović, Đurđe, Srivastava, H. M., "Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function" in Applied Mathematics Letters, 22, no. 7 (2009):1081-1084, https://doi.org/10.1016/j.aml.2008.08.024 . .
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