分部求和法
分部求和法（英语：Summation by parts）也叫阿贝尔变换（英语：Abel transformation，有别于Abel transform）或阿贝尔引理（英语：Abel's lemma）是求和的一种方法。设
和
为两个数列，则有
![\sum_{k=m}^n f_k(g_{k+1g_k) = \left[f_{n}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1 f_k)](/uploads/202412/16/a11c6a929fabfdf367655277189398173611.png)
.
它被用来证明积分第二中值定理。
分部求和公式也可被写成比较对称的方式：
Abel transform
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Abel transform 分部求和公式
In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by:
Assuming f(r) drops to zero more quickly than 1/r, the inverse Abel transform is given by
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