Examples for and

Let the pseudo- as

 

This function is a continuous function. Therefore, we can study this with differential calculus. In the limit ( ) the equation approaches function. For example,under the condition (y<x),

Using (3), is given by

 

These functions are easily extended to the general cases in which N-variable and also have parameterized pseudo expression as follows. N-variable pseudo- is given by

 

Similarly, N-variable pseudo- is given by

 

We can easily confirm these functions (6)-(7) approach N-variable and respectively under the limit ( ). For example,