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Explore the intricacies of the Riemann-Zeta function in this 26-minute video lecture. Begin with an introduction to this fundamental mathematical concept, then delve into the derivation of a generating function for its values at positive even integers. Utilize this generating function to prove two significant sum identities. Gain valuable insights from mathematics expert Michael Penn, affiliated with Randolph College. Enhance your understanding of complex mathematical concepts and their applications in number theory and analysis.