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:

Read more about this topic:  Dirichlet Eta Function

Famous quotes containing the word values:

    “Despite the hundreds of attempts, police terror and the concentration camps have proved to be more or less impossible subjects for the artist; since what happened to them was beyond the imagination, it was therefore also beyond art and all those human values on which art is traditionally based.”
    —A. Alvarez (b. 1929)

    “The traveller who has gone to Italy to study the tactile values of Giotto, or the corruption of the Papacy, may return remembering nothing but the blue sky and the men and women who live under it.”
    —E.M. (Edward Morgan)