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Contour integral representations for Riemann's Zeta function and Dirichelet'sEta (alternating Zeta) function are presented and investigated. Theserepresentations flow naturally from methods developed in the 1800's, butsomehow they do not appear in the standard reference summaries, textbooks orliterature. Using these representations as a basis, alternate derivations ofknown series and integral representations for the Zeta and Eta function areobtained on a unified basis that differs from the textbook approach, andresults are developed that appear to be new.

Integral and Series Representations of Riemann's Zeta function, Dirichelet's Eta Function and a Medley of Related Results