This form uses the theory of beams in bending as represented by the equation M=-EJy'' with added the effect of shear deflection given by y'=χT/GA
The solution is based onto a polynomial approximation formula obtained from strain energy V minimization (choose 'Show formulae' under 'Options' to see, relationships enforcing boundary conditions not shown).
Note that the deflection due to shear is normally negligible, however in some cases it may help to have a finer picture of beam behavior.