Is this function ∑ k ≥ 1 1 ( 2 k − 1 ) s , R e ( s ) &gt; 1is well known?

Question

Is this function      ∑          k      ≥      1            1                  (        2        k        −        1        )                    s              ,    R  e  (  s  )  &amp;gt;  1is well known?

Dayana Zuniga · Accepted Answer

Formally,  ζ      (    s    )    =      ∑          k      =      1              +      ∞            1          k              s              =      ∑          k      =      1              +      ∞            1                  (        2        k        )                    s              +      ∑          k      =      1              +      ∞            1                  (        2        k        −        1        )                    s              =      1          2              s                  ∑          k      =      1              +      ∞            1          k              s              +      ∑          k      =      1              +      ∞            1                  (        2        k        −        1        )                    s            whence      ∑          k      =      1              +      ∞            1                  (        2        k        −        1        )                    s              =  ζ      (    s    )        (    1    −          1              2                  s                      )    .

Is this function <munder> <mo movablelimits="false">∑ k &#

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