Zeta Constant - Sum of Zeta Constants

Sum of Zeta Constants

The following sums can be derived from the generating function:

where is the digamma function.

Series related to the Euler–Mascheroni constant (denoted by γ) are

and using the principle value (which of course effects only the value at 1) these formulae can be stated nicer as

and show that they "live" only because the principle value of .

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