Abel's theorem

This article is about Abel's theorem on power series. For Abel's theorem on algebraic curves, see Abel–Jacobi map. For Abel's theorem on the Insolvability of the quintic equation, see Abel–Ruffini theorem. For Abel's theorem on linear differential equations, see Abel's identity. For Abel's theorem on irreducible polynomials, see Abel's irreducibility theorem. For Abel's formula for summation of a series, using an integral, see Abel's summation formula.

In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel, who proved it in 1826.[1]

  1. ^ Abel, Niels Henrik (1826). "Untersuchungen über die Reihe u.s.w.". J. Reine Angew. Math. 1: 311–339.