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I have been attempting to integrate the Gram series, G(x), which is defined in the following link: http://mathworld.wolfram.com/GramSeries.html. I have been trying to find methods to integrate this series, as it is an approximation to Pi(x). Does anyone have any suggestions?

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Make the substitution $e^x$ and integrate term by term. –  Ethan Jul 6 '13 at 7:03
    
When you say substitute do you mean replace x for e^x? This doesn't greatly improve the method of solving this, though. –  Nihal Jul 6 '13 at 9:31
    
how did Gramm got his Gramm series ?? –  Jose Garcia Aug 7 '13 at 15:01
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