Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I am surprised. Do you mean that somehow an analytic continuation is being made automagically ? This sum is divergent when the real part of s is smaller than 1. For k=2, the values at negative integers are known to be (0: -1/3), (-1: -1/60), (-2: 1/315), (-3: -1/840), (-4: 1/1155). Do you get those ?
