We know that the arctan series $\sum\limits_{n = 1}^\infty {\arctan \left( {\frac{{2{a^2}}}{{{n^2}}}} \right)} $ exist closed form, see enter link description here. Similarly, my question is that the arctan series of the form $$\sum\limits_{n = 1}^\infty {\frac{{\arctan \left( {\frac{1} {{{n^p}}}} \right)}} {{{n^q}}}}=? ,\;p + q \geqslant 2.$$ It exist closed form?
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