What type of kernel density function does ArcMap use?
Silverman quadratic "The kernel function is based on the quadratic kernel function described in Silverman (1986, p. 76, equation 4.5)."
http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/How_Kernel_Density_works/009z00000011000000/
The reference is to this book:
http://books.google.com/books?id=e-xsrjsL7WkC&printsec=frontcover#v=onepage&q&f=false
on page 76, equation 4.5