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If a real or complex power series for a function has radius of convergence 1 and the series is only known to converge conditionally at 1, Abel's limit theorem gives the value at 1 as the limit of the function at 1 from the left. "Left" for complex numbers means within a fixed cone opening to the left with angle less than | If a real or complex power series for a function has radius of convergence 1 and the series is only known to converge conditionally at 1, Abel's limit theorem gives the value at 1 as the limit of the function at 1 from the left. "Left" for complex numbers means within a fixed cone opening to the left with angle less than π. | ||
Revision as of 14:15, 26 May 2025
Encyclopedia of MathematicsAbel_summation_methodWikiDataQ318767MaRDI QIDQ6481641
theorem
Named after: Niels Henrik Abel
This page was built for theorem: Abel's theorem
If a real or complex power series for a function has radius of convergence 1 and the series is only known to converge conditionally at 1, Abel's limit theorem gives the value at 1 as the limit of the function at 1 from the left. "Left" for complex numbers means within a fixed cone opening to the left with angle less than π.
