Is Catalan’s Constant Rational?
Abstract
:1. Introduction
2. Left-Hand Side Contour Integral
3. The Hurwitz Zeta Function
4. Contour Integral Representations for the Hurwitz Zeta Function
4.1. Derivation of the First Contour Integral
4.2. Derivation of the Second Contour Integral
5. The Infinite Sum of the Euler Polynomial in Terms of Hurwitz Zeta Function
5.1. Catalan’s Constant in Terms of the Euler’s Polynomial
5.2. An Open Problem
5.3. The Derivative with Respect to k
6. Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Reynolds, R.; Stauffer, A. Is Catalan’s Constant Rational? Mathematics 2022, 10, 4251. https://doi.org/10.3390/math10224251
Reynolds R, Stauffer A. Is Catalan’s Constant Rational? Mathematics. 2022; 10(22):4251. https://doi.org/10.3390/math10224251
Chicago/Turabian StyleReynolds, Robert, and Allan Stauffer. 2022. "Is Catalan’s Constant Rational?" Mathematics 10, no. 22: 4251. https://doi.org/10.3390/math10224251
APA StyleReynolds, R., & Stauffer, A. (2022). Is Catalan’s Constant Rational? Mathematics, 10(22), 4251. https://doi.org/10.3390/math10224251