Abel's theorem — An Etymological Dictionary of Astronomy and Astrophysics

Abel's theorem

فربین ِ آبل

farbin-e Abel

Fr.: théorème d'Abel

If a → power series → converges for some nonzero value x₀, then it converges absolutely for any value of x, for which |x| < |x₀|.
If a power series → diverges for some nonzero value x₀, then it diverges for any value of x, for which |x| > |x₀|.

See also: Named after the Norwegian mathematician Niels Henrik Abel (1802-1829); → theorem.

An Etymological Dictionary of Astronomy and Astrophysics