Solve only question $2$ in python code.

The Cardinal B$-$splines are those with integer knots $t_k=k$ for kinZ.

$(1)$ Use the recursion formula for B$-$splines to compute the piecewise polynomial form for the cardinal B$-$Splines $N_0^k$ of orders $k=1,2,3,4,$ by hand calculation. Write these using the 'case' statement.

$(2)$ Write a function m$-$file "function $y=$ncppval$(k,t)"$ in Matlab $($or Python definition$)$ to evaluate these cardinal B$-$splines with vector input $t,$ and plot them, for $k=1,$dots,$4.$ Use the expressions you found in the first problem.