title: Computation of numerical integral involving convolution
body: <p>I have to solve the following convolution related numerical integration problem in R or perhaps computer algebra system like Maxima.<br>
  <strong>Integral[({k(y)-l(y)}^2)dy]</strong><br>
  where<br>
   k(.) is the pdf of a standard normal distribution<br>
  l(y)=integral[k(z)*k(z+y)dz] (standard convolution)<br>
  z and y are scalars<br>
  The domain of y is -inf to +inf.<br>
  The integral in function l(.) is an indefinite integral. Do I need to add any additional assumption on z  to obtain this?<br>
  Thank you.</p>