I'm attempting to perform interpolation in 3 dimensions and have a question that hopefully someone can answer. The derivative approximation is simple in a single direction: df/dx(i,j,k)= [f(i+1,j,k) - f(i-1,j,k)] / 2 And I know that in the second order: d2f/dxdy(i,j,k)= [f(i+1,j+1,k) - f(i+1,j,k) - f(i,j+1,k) + f(i-1,j-1,k)] / 4 The final item I need is the third order approximation, and I'm not sure how to scale the first two into a third variable. d3f/dxdydz(i,j,k)= ? Can anyone shed some light on this? Thanks in advance!