利用母函数法证明组合恒等式

Proof of combinatirial Identity by Using General Funcfion Method

简单的组合恒等式可以由多重集的排列、组合的定义直接发现并且证明,但对于一些复杂的组合恒等式,这种方法就显得无能为力.本文利用母函数法这个强有力的工具,首先列举了一些常见序列的母函数,然后利用它们证明了一类较为复杂的组合恒等式.

Some simple combinatirial identities can be directly found and proved by the definition of permutations and combinations, but some compbicated ones can not be solved like this. In this paper, some common genecal function have been enumerafed at first, then a class of more complicated combinatirial identities be proved by this powerful fools - general function method.