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,