In the attached image is the python problem.

and here is the defining:

#input data $($need to have x$\_\{$i$+1\}-$ x$\_$i $=1)$ for simplest model

#output polynomial

def build$\_$polyonomial$($D$)$:

#Implement difference operator for values in list: lst at index x

def delta$($lst$,$ x$)$:

pass

#Implement the delta operator on lst

def Delta$($lst$)$:

pass

#Create and return the difference table

def dtable$($lst$)$:

pass

#build rho

def rho$($lst$)$:

pass

#build binomial function

def prod$($n$)$:

pass

# return for the build polynomial should go here

pass

Thank you for your help!