  The history of linear differential equations is over 350 years. By using
Frobenius method and putting the power series expansion into linear
differential equations, the recursive relation of coefficients starts to
appear. There can be between two and infinity number of coefficients in the
recurrence relation in the power series expansion. During this period
mathematicians developed analytic solutions of only two term recursion relation
in closed forms. Currently the analytic solution of three term recurrence
relation is unknown. In this paper I will generalize the three term recurrence
relation in the linear differential equation. This paper is 2nd out of 10 in
series "Special functions and three term recurrence formula (3TRF)". The next
paper in series deals with the power series expansion in closed forms of Heun
function by Choun [arXiv:1303.0830]. The rest of the papers in the series show
how to solve mathematical equations having three term recursion relations and
go on producing the exact solutions of some of the well known special functions
including: Mathieu, Heun, Biconfluent Heun and Lame equations. See section IX
for all the papers and short descriptions in the series.
