  In this article, we calculate the period determinant of an irrgular singular
connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate
its de Rham cohomology and the cycles in the homology of the dual connection
and describe the period matrix. Terasoma's work is introduced to approximate
the direct image connection pi_*(\nabla) by a sequence of regular connections
as an intermediate step where pi:U -> A^1(y), (x,y) |-> y. Finally, we will
compare the period obtained by this approximation of the direct image
connection and the original.
