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proof explanation - Value of the Riemann Zeta Function for

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I am reading the book "Riemann's Zeta Function" by H. M. Edwards. I had a confusion in Section 1.5, Page 12 at the derivation of the formula of Riemann Zeta Function at negative integers

13. The Riemann zeta function is defined for real

The Secrets Of The Universe - #Equations#40 The 40th Equation of the series is on the famous Riemann Zeta Function. This function first appeared in the first half of the 18th century

Riemann zeta function 1

Riemann Zeta Function -- from Wolfram MathWorld

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Riemann hypothesis, Prime Numbers, Zeta Function & Complex Analysis

1: Real and imaginary part and absolute value of Riemann zeta function

Particular values of the Riemann zeta function - Wikipedia

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