Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results
Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results
Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of …