Integral representations for certain series
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- by Xue-Feng Duan and Ruiming Zhang
- Proc. Amer. Math. Soc. 150 (2022), 2487-2497
- DOI: https://doi.org/10.1090/proc/15853
- Published electronically: March 7, 2022
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Abstract:
In this work we apply the classical Plana summation formula to derive integral representations for certain infinite series that their general terms containing Gamma, $q$-Gamma, theta, Bessel, and Hurwitz zeta functions.References
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Bibliographic Information
- Xue-Feng Duan
- Affiliation: School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, People’s Republic of China
- Email: guidian520@126.com
- Ruiming Zhang
- Affiliation: School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, People’s Republic of China
- MR Author ID: 257230
- Email: ruimingzhang@guet.edu.cn
- Received by editor(s): June 17, 2021
- Received by editor(s) in revised form: September 7, 2021
- Published electronically: March 7, 2022
- Additional Notes: The first author’s research was supported by the National Natural Science Foundation of China No. 11761024. The second author’s research was supported by National Natural Science Foundation of China, grant No. 11771355
The second author is the corresponding author - Communicated by: Mourad Ismail
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2487-2497
- MSC (2020): Primary 33D99
- DOI: https://doi.org/10.1090/proc/15853
- MathSciNet review: 4399265