The three tables of finite difference coefficients are generated by fdcoefficient.
Central finite difference
| n | m | -5 | -4 | -3 | -2 | -1 | +0 | +1 | +2 | +3 | +4 | +5 |
|---|
| 1 | 2 | | | | | -1/2 | 0 | 1/2 | | | | |
| 1 | 4 | | | | 1/12 | -2/3 | 0 | 2/3 | -1/12 | | | |
| 1 | 6 | | | -1/60 | 3/20 | -3/4 | 0 | 3/4 | -3/20 | 1/60 | | |
| 1 | 8 | | 1/280 | -4/105 | 1/5 | -4/5 | 0 | 4/5 | -1/5 | 4/105 | -1/280 | |
| 2 | 2 | | | | | 1 | -2 | 1 | | | | |
| 2 | 4 | | | | -1/12 | 4/3 | -5/2 | 4/3 | -1/12 | | | |
| 2 | 6 | | | 1/90 | -3/20 | 3/2 | -49/18 | 3/2 | -3/20 | 1/90 | | |
| 2 | 8 | | -1/560 | 8/315 | -1/5 | 8/5 | -205/72 | 8/5 | -1/5 | 8/315 | -1/560 | |
| 3 | 2 | | | | -1/2 | 1 | 0 | -1 | 1/2 | | | |
| 3 | 4 | | | 1/8 | -1 | 13/8 | 0 | -13/8 | 1 | -1/8 | | |
| 3 | 6 | | -7/240 | 3/10 | -169/120 | 61/30 | 0 | -61/30 | 169/120 | -3/10 | 7/240 | |
| 3 | 8 | 41/6048 | -1261/15120 | 541/1120 | -4369/2520 | 1669/720 | 0 | -1669/720 | 4369/2520 | -541/1120 | 1261/15120 | -41/6048 |
| 4 | 2 | | | | 1 | -4 | 6 | -4 | 1 | | | |
| 4 | 4 | | | -1/6 | 2 | -13/2 | 28/3 | -13/2 | 2 | -1/6 | | |
| 4 | 6 | | 7/240 | -2/5 | 169/60 | -122/15 | 91/8 | -122/15 | 169/60 | -2/5 | 7/240 | |
| 4 | 8 | -41/7560 | 1261/15120 | -541/840 | 4369/1260 | -1669/180 | 1529/120 | -1669/180 | 4369/1260 | -541/840 | 1261/15120 | -41/7560 |
Forward finite difference
| n | m | +0 | +1 | +2 | +3 | +4 | +5 | +6 | +7 |
|---|
| 1 | 1 | -1 | 1 | | | | | | |
| 1 | 2 | -3/2 | 2 | -1/2 | | | | | |
| 1 | 3 | -11/6 | 3 | -3/2 | 1/3 | | | | |
| 1 | 4 | -25/12 | 4 | -3 | 4/3 | -1/4 | | | |
| 2 | 1 | 1 | -2 | 1 | | | | | |
| 2 | 2 | 2 | -5 | 4 | -1 | | | | |
| 2 | 3 | 35/12 | -26/3 | 19/2 | -14/3 | 11/12 | | | |
| 2 | 4 | 15/4 | -77/6 | 107/6 | -13 | 61/12 | -5/6 | | |
| 3 | 1 | -1 | 3 | -3 | 1 | | | | |
| 3 | 2 | -5/2 | 9 | -12 | 7 | -3/2 | | | |
| 3 | 3 | -17/4 | 71/4 | -59/2 | 49/2 | -41/4 | 7/4 | | |
| 3 | 4 | -49/8 | 29 | -461/8 | 62 | -307/8 | 13 | -15/8 | |
| 4 | 1 | 1 | -4 | 6 | -4 | 1 | | | |
| 4 | 2 | 3 | -14 | 26 | -24 | 11 | -2 | | |
| 4 | 3 | 35/6 | -31 | 137/2 | -242/3 | 107/2 | -19 | 17/6 | |
| 4 | 4 | 28/3 | -111/2 | 142 | -1219/6 | 176 | -185/2 | 82/3 | -7/2 |
Backward finite difference
| n | m | -7 | -6 | -5 | -4 | -3 | -2 | -1 | +0 |
|---|
| 1 | 1 | | | | | | | -1 | 1 |
| 1 | 2 | | | | | | 1/2 | -2 | 3/2 |
| 1 | 3 | | | | | -1/3 | 3/2 | -3 | 11/6 |
| 1 | 4 | | | | 1/4 | -4/3 | 3 | -4 | 25/12 |
| 2 | 1 | | | | | | 1 | -2 | 1 |
| 2 | 2 | | | | | -1 | 4 | -5 | 2 |
| 2 | 3 | | | | 11/12 | -14/3 | 19/2 | -26/3 | 35/12 |
| 2 | 4 | | | -5/6 | 61/12 | -13 | 107/6 | -77/6 | 15/4 |
| 3 | 1 | | | | | -1 | 3 | -3 | 1 |
| 3 | 2 | | | | 3/2 | -7 | 12 | -9 | 5/2 |
| 3 | 3 | | | -7/4 | 41/4 | -49/2 | 59/2 | -71/4 | 17/4 |
| 3 | 4 | | 15/8 | -13 | 307/8 | -62 | 461/8 | -29 | 49/8 |
| 4 | 1 | | | | 1 | -4 | 6 | -4 | 1 |
| 4 | 2 | | | -2 | 11 | -24 | 26 | -14 | 3 |
| 4 | 3 | | 17/6 | -19 | 107/2 | -242/3 | 137/2 | -31 | 35/6 |
| 4 | 4 | -7/2 | 82/3 | -185/2 | 176 | -1219/6 | 142 | -111/2 | 28/3 |