Sum this infinite series: sum[-infty,+infty] 1/(n^2+n+1) (w/ tan(h) appearing)

Jingtingbai

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Apr 1, 2018
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Can anyone help me with summing this infinite series:

. . . . .\(\displaystyle \displaystyle \sum_{-\infty}^{\infty}\, \dfrac{1}{n^2\, +\, n\, +\, 1}\)

with the function tan(h) appearing as a major factor in the result? Thanks a lot!
 
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