Is Catalan’s Constant Rational?

Abstract

This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the Riemann Zeta function and fundamental mathematical constants, including Catalan’s constant. This representation of Catalan’s constant suggests it could be rational.

Keywords

• Euler polynomial
• Catalan’s constant
• Hurwitz Zeta function
• Cauchy integral
• Apéry’s constant