Proof. Let us suppose that the k-Jacobsthal-Lucas numbers are the coef-
ficients of a power series centered at the origin, that is convergent in
− 1
r1
,
1
r1
,
taking in account the Proposition (2.5) . To the sum of this power series, jk(x),
we call generating function of the k-Jacobsthal-Lucas numbers. So we have