On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c
For k∈ℤ, the generalized Arakawa–Kaneko zeta functions with a, b, c parameters are given by the Laplace-Mellin integral ξks,x;a,b,c=1/Γs∫0∞Lik1−ab−t/bt−a−tc−xtts−1dt, where ℜs>0 and x>0 if k≥1, and ℜs>0 and x>k+1 if k≤0. In this paper, an interpolation formula between these generalized z...
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Hindawi Limited
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/2041262 |
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doaj-8ac7212d33484107a29d76ef11ca77322020-11-25T03:52:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/20412622041262On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,cNestor G. Acala0Edward Rowe M. Aleluya1Mathematics Department, College of Natural Sciences and Mathematics, Mindanao State University-Main Campus, Marawi, Lanao Del Sur, PhilippinesDepartment of Physical Sciences and Mathematics, College of Science and Environment, Mindanao State University-Naawan, Naawan, Misamis Oriental, PhilippinesFor k∈ℤ, the generalized Arakawa–Kaneko zeta functions with a, b, c parameters are given by the Laplace-Mellin integral ξks,x;a,b,c=1/Γs∫0∞Lik1−ab−t/bt−a−tc−xtts−1dt, where ℜs>0 and x>0 if k≥1, and ℜs>0 and x>k+1 if k≤0. In this paper, an interpolation formula between these generalized zeta functions and the poly-Bernoulli polynomials with a,b,c parameters is obtained. Moreover, explicit, difference, and Raabe’s formulas for ξks,x;a,b,c are derived.http://dx.doi.org/10.1155/2020/2041262 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nestor G. Acala Edward Rowe M. Aleluya |
| spellingShingle |
Nestor G. Acala Edward Rowe M. Aleluya On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Nestor G. Acala Edward Rowe M. Aleluya |
| author_sort |
Nestor G. Acala |
| title |
On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_short |
On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_full |
On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_fullStr |
On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_full_unstemmed |
On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_sort |
on generalized arakawa–kaneko zeta functions with parameters a,b,c |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2020-01-01 |
| description |
For k∈ℤ, the generalized Arakawa–Kaneko zeta functions with a, b, c parameters are given by the Laplace-Mellin integral ξks,x;a,b,c=1/Γs∫0∞Lik1−ab−t/bt−a−tc−xtts−1dt, where ℜs>0 and x>0 if k≥1, and ℜs>0 and x>k+1 if k≤0. In this paper, an interpolation formula between these generalized zeta functions and the poly-Bernoulli polynomials with a,b,c parameters is obtained. Moreover, explicit, difference, and Raabe’s formulas for ξks,x;a,b,c are derived. |
| url |
http://dx.doi.org/10.1155/2020/2041262 |
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AT nestorgacala ongeneralizedarakawakanekozetafunctionswithparametersabc AT edwardrowemaleluya ongeneralizedarakawakanekozetafunctionswithparametersabc |
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1715097266156470272 |