From: mikechurch72@gmail.com   
      
   I'm studying neural networks and had reason to seek a value c s.t. the   
   variance of arctan( c*x ), where x ~ N(0, 1), is 1. For my purposes, c   
   = 5/2 was good enough (variance of 1.000321...) but I wanted to find   
   out what the actual value of this 'c' was.   
      
   It would be the value of c for which the integral INT(   
   exp(-x^2/2)*atan(c*x)^2, x, -inf, inf ) has value 1. I used some   
   numerical methods in Java to run the relevant integral (delta =   
   .000001; bounds -10 to 10) for various values of c and found c =   
   2.49876176...   
      
   Is there any analytically meaningful value to this number? Is it   
   familiar to anyone? There's no practical reason for me to have any   
   interest in this, but I do find myself oddly curious.   
      
   -Mike Church   
   http://ambition-game.blogspot.com/   
      
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