Consider that a 1-D domain is heated by a pulsing laser heating source irradiating at X = 0 along the X direction, with the heating source given by Show that the analytic solution for the temperature...

Consider that a 1-D domain is heated by a pulsing laser heating source irradiating at X = 0 along the X direction, with the heating source given by

Show that the analytic solution for the temperature distribution takes the following form:

Here, the Green function ) ~ , ~ G(X ,[ | X [ is in the form of

where X_L
is the dimensionless length of the solid,
 and N is the number of the terms when E is changing from positive to negative.