类Vandermonde恒等式的新组合恒等式:第一部分

Novel combinatorial identities analogous to those of Vandermonde, part Ⅰ

Vandermonde卷积恒等式为n∑k=0(xk)(yn-k)=(x+yn),其中x和y为复数,n为非负整数.本文研究如下形式n∑k=0(x k)(y k)=(x+yn)+R(x,y,n)与其他相关扩充的关系.

The Vandermonde convolution identity states thatn∑k=0（x k）（y n- k）=（x ＋ y n）,valid for all complex x and y, and all integers n 0. In this paper we investigate relations of the formn∑k=0（x k）（y k）=（x ＋ y n）＋ R（x, y, n）and other related expansions.