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The definitions used here don't seem to be standard. What the author of the piece has called a "homogeneous Fredholm equation of the first kind" is simply a "Fredholm equation of the first kind". The second kind of Fredholm equation comes in two flavours, homogeneous (if f=0) or inhomogeneous. See e.g. the text book by Tricomi ("Integral Equations", Interscience, 1957,page 3. —Preceding unsigned comment added by 192.171.166.244 (talk) 13:59, 14 September 2009 (UTC)