Dirichlet Eta Function - Particular Values

Particular Values

Further information: Zeta constant
  • η(0) = 1⁄2, the Abel sum of Grandi's series 1 − 1 + 1 − 1 + · · ·.
  • η(−1) = 1⁄4, the Abel sum of 1 − 2 + 3 − 4 + · · ·.
  • For k an integer > 1, if Bk is the k-th Bernoulli number then

Also:

, this is the alternating harmonic series
 A072691

The general form for even positive integers is:

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