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T. Amdeberhan
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Closed formula for a certain infinite series

I came across this problem while doing some simplifications.

So, I like to ask

QUESTION. Is there a closed formula for the evaluation of this series? $$\sum_{(a,b)=1}\frac{\cos\left(\frac{a}b\right)}{a^2b^2}$$ where the sum runs over all pairs of positive integers that are relatively prime.

T. Amdeberhan
  • 43.2k
  • 5
  • 57
  • 217