summation by parts

For the formula on difference operators, see Summation by parts.

Summation by parts is also frequently used to prove Abel's theorem.

One can also formulate a discrete analogue for sequences, called summation by parts.

From summation by parts, we have that .

The summation by parts formula is sometimes called Abel's lemma or Abel transformation.

Indefinite summation by parts:

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.

Was previously studied by Weyl himself, he developed a method to express the sum as the value , where 'G' can be defined via a linear differential equation similar to Dyson equation obtained via summation by parts.