Find the summation of this series :

$\displaystyle \sum_{k=1}^{\infty} \tan^{-1}[ \frac{ y^2 }{ k^2 + x^2 } ]$

Quote:

Consider $\displaystyle sinx = x \prod_{j=1}^{\infty} [ 1 - \frac{x^2}{(j \pi)^2}]$

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- May 2nd 2009, 01:53 AMsimplependuluminfinite series
Find the summation of this series :

$\displaystyle \sum_{k=1}^{\infty} \tan^{-1}[ \frac{ y^2 }{ k^2 + x^2 } ]$

Quote:

Consider $\displaystyle sinx = x \prod_{j=1}^{\infty} [ 1 - \frac{x^2}{(j \pi)^2}]$