We show that the section determinant of $e^A$ can be expressed, under certain conditions, by the Fredholm determinant of an integral operator. The kernel function of this integral operator is computed explicitly in terms of the operator $A$. As a simple consequence we derive a Weierstrass type product expansion for the section determinant.

Section determinant, group of operators, exponential function of operators, Fredholm determinant

47D03 (15A15, 47B10)