Abstract and Applied Analysis

Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series

Jorge Sanchez-Ortiz

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Abstract

In this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series.

Article information

Source
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 4875916, 5 pages.

Dates
Received: 5 September 2018
Accepted: 29 November 2018
First available in Project Euclid: 10 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1547089413

Digital Object Identifier
doi:10.1155/2018/4875916

Mathematical Reviews number (MathSciNet)
MR3894338

Zentralblatt MATH identifier
07029289

Citation

Sanchez-Ortiz, Jorge. Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series. Abstr. Appl. Anal. 2018 (2018), Article ID 4875916, 5 pages. doi:10.1155/2018/4875916. https://projecteuclid.org/euclid.aaa/1547089413


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