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Thursday, September 22, 2016

Entry 9

Here is another "bizarre" continued fraction from Ramanujan involving e and π. For x>0 πex2x=1+x13+x2135+x31357++1x+11+2x+31+As Kevin Brown of Mathpages commented in this old sci.math post, "Is there any other mathematician whose work is instantly recognizable?" Note that the error function has a reminiscent form (also rediscovered by Ramanujan) x0et2dt=12πerf(x)=12π1x+12x+2x+32x+

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