This function replaces y=|x|n in the interval -δ...+δ by a 4-th order polynomial that has the same function value and the first and second derivative at x=± δ.
A typical use of this function is to replace the function for the convective heat transfer coefficient for forced or free convection that is of the form h=c |dT|n for some constant c and exponent 0 ≤ n ≤ 1. By using this function, the original function that has an infinite derivative near zero and that takes on zero at the origin is replaced by a function with a bounded derivative and a non-zero value at the origin. Physically, the region -δ...+δ may be interpreted as the region where heat conduction dominates convection in the boundary layer.
See the packageExamples for the graph.