Motion of electrons in a half space with cylindrical electro-static field,
which is associated with electron emission devices, is investigated. The eq
uation of motion is given as a nonlinear ordinary differential equation of
the second order, Statistical behavior of electrons exhibits a dilatational
invariance property of the system. An approximate formula of absorbed poin
ts distribution of the electrons is given by the solution of a Fredholm int
egral equation of the second kind. Since its kernel function is [0, 1) char
acteristrics function, we give its finite sum expression using the properti
es of B-spline, which is the iterated kernel function of its Neumann series
solution.