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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| Format: | Article |
| Language: | English |
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Wiley
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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| author | Nestor G. Acala Edward Rowe M. Aleluya |
| author_facet | Nestor G. Acala Edward Rowe M. Aleluya |
| author_sort | Nestor G. Acala |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8ac7212d33484107a29d76ef11ca7732 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8ac7212d33484107a29d76ef11ca77322025-02-03T06:43:50ZengWileyInternational 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 |
| 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 |
| title | 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_short | On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c |
| title_sort | on generalized arakawa kaneko zeta functions with parameters a b c |
| url | http://dx.doi.org/10.1155/2020/2041262 |
| work_keys_str_mv | AT nestorgacala ongeneralizedarakawakanekozetafunctionswithparametersabc AT edwardrowemaleluya ongeneralizedarakawakanekozetafunctionswithparametersabc |