  A new analytical operator method is discussed which solves linear ordinary
differential equations with regular singularities. Solutions are obtained in
analytic series form and also in Mellin-Barnes-type contour integral form.
Exact series solution is obtained without having to calculate series
coefficients by recurrence relation.Both homogeneous and inhomogeneous
equations are solved identically without having to calculate the Green's
function explicitly in the case of inhomogeneous equation.Closed-form solutions
are obtained for all the special functions appearing in mathematical physics.
For a second-order equation both the independent solutions are obtained without
invoking Wronskians, even when the indices differ by an integer.
