Plot[BSplineBasis[0,x+1/2],{x,-1,1},PlotLabel->B0]

PiecewiseExpand[BSplineBasis[0,x+1/2]]

Plot[BSplineBasis[1,x/2+1/2],{x,-2,2},PlotLabel->B1]

PiecewiseExpand[BSplineBasis[1,x/2+1/2]]

Plot[BSplineBasis[2,x/3+1/2],{x,-2,2},PlotLabel->B2]

PiecewiseExpand[BSplineBasis[2,x/3+1/2]]

Plot[BSplineBasis[3,x/4+1/2],{x,-2,2},PlotLabel->B3]

PiecewiseExpand[BSplineBasis[3,x/4+1/2]]