将f?x?按第n?1列展开，得
f?x??A1,n?1?A2,n?1x???An,n?1xn?1?An?1,n?1xn，
其中，xn?1的系数为
An,n?1???1?n??n?1?Dn??Dn.
又根据范德蒙德行列式的结果知
f?x???x?x1??x?x2???x?xn?由上式可求得xn?1的系数为
1?j?i?n??xi?xj?.
??x1?x2?xn?故有
1?j?i?n??xi?xj?.
Dn??x1?x2???xn?
1?j?i?n??xi?xj?.
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将f?x?按第n?1列展开，得
f?x??A1,n?1?A2,n?1x???An,n?1xn?1?An?1,n?1xn，
其中，xn?1的系数为
An,n?1???1?n??n?1?Dn??Dn.
又根据范德蒙德行列式的结果知
f?x???x?x1??x?x2???x?xn?由上式可求得xn?1的系数为
1?j?i?n??xi?xj?.
??x1?x2?xn?故有
1?j?i?n??xi?xj?.
Dn??x1?x2???xn?
1?j?i?n??xi?xj?.
25