Abel Summation

A summation-by-parts identity (discrete Abel transform) that relates sums of the form sum_{n ≤ x} a_n b_n to the partial sums A(t)=sum_{n ≤ t} a_n and discrete differences of b, typically written as sum_{n≤x} a_n b_n = A(x) b_x - ∫_{1}^{x} A(t) d b(t), and used to transfer asymptotic information between sequences and weighted sums.