Simply applying the results shown in equation 3.5 within
equation 3.1 gives a form of 
which appears as a sum of three
overlap--type integrals with various multiplicative constants. To display the
particular overlap integrals involved in that sum we will use a particular notation
derived from the bra and ket notation common in physics. Let
denote a gaussian where the angular momentum has
been increased or decreased by n in the 
coordinate. In other
words,
Thus, given that the overlap between two gaussians 
and 
is
the construction 
denotes an overlap integral between
and a gaussian derived from 
by incrementing the exponent of x
by 2. In this way, we can write the asymmetric form of the kinetic energy
integral using equations 3.2 and 3.5 as
I havn't yet got this to work in my program.