Uniform Distribution as the Limiting Form of a Density Function

The uniform distribution, denoted by U(x;A,B)=1/(B-A) if 0<A<x<B<∞ and zero otherwise, is the simplest probability density functions of a continuous random variable X. For X on interval (0, 1), three parameters function, h(x;A,B,n), constructed so that its limiting form function U(x;A,B) in which n→∞.