Abel's summation formula, introduced by the Norwegian mathematician Niels Henrik Abel, is a technique for computing series that is used heavily in analytic number theory and in the study of special functions. It relates a sum involving a sequence of terms to an integral involving the sequence's partial sums, letting a discrete sum be analyzed with the tools of continuous calculus. The same name is also sometimes applied to two related but distinct ideas, summation by parts and the Abel-Plana formula.
Facts
Connections
Attributed To
Source Abel's Summation Formula (Wikipedia)
In Branch
Source Abel's Summation Formula (Wikipedia)
Is Kind Of Object
Named After
Sources
1. Abel's Summation Formula (Wikipedia)
Lead section
In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in analytic number theory and the study of special functions to compute series.
In Branch: Analytic Number Theory, Lead sentence
uced by Niels Henrik Abel, is intensively used in analytic number theory and the study of special functions to compute series.
Attributed To: Niels Henrik Abel, Lead paragraph
introduced by Niels Henrik Abel
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.