Editing Dirichlet eta function (section)

==Particular values==
{{further|Zeta constant}}
*''η''(0) = {{1/2}}, the [[Abel summation|Abel sum]] of [[Grandi's series]] 1 − 1 + 1 − 1 + ⋯.
*''η''(−1) = {{1/4}}, the Abel sum of [[1 − 2 + 3 − 4 + ⋯]].
*For positive integer ''k'',
<math display="block">\eta(1-k) = \frac{2^k-1}{k} B^{+{}}_k,</math> where {{math|''B''{{su|p=+|b=''n''}}}} is the ''k''-th [[Bernoulli number]].

Also:
*<math>\eta(1) = \ln2 </math>, this is the [[alternating harmonic series]]
*<math>\eta(2) = {\pi^2 \over 12} </math> {{OEIS2C|A072691}}
*<math>\eta(4) = {{7\pi^4} \over 720} \approx 0.94703283</math>
*<math>\eta(6) = {{31\pi^6} \over 30240} \approx 0.98555109</math>
*<math>\eta(8) = {{127\pi^8} \over 1209600} \approx 0.99623300</math>
*<math>\eta(10) = {{73\pi^{10}} \over 6842880} \approx 0.99903951</math>
*<math>\eta(12) = {{1414477\pi^{12}} \over {1307674368000}} \approx 0.99975769</math>

The general form for even positive integers is:
<math display="block">\eta(2n) = (-1)^{n+1}{{B_{2n}\pi^{2n} \left(2^{2n-1} - 1\right)} \over {(2n)!}}. </math>

Taking the limit <math>n \to \infty</math>, one obtains <math>\eta (\infty) = 1</math>.