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.
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Abel's Summation Formula
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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.
Principal Result Of: Niels Henrik Abel, Lead sentence of the article on the result
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
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