Abel sum

Meaning

Noun

• Given a power series $f(x)=\; \backslash sum\_\{n=0\}^\backslash infty\; a\_n\; x^n$ that is convergent for real x in the open interval (0, 1), the value $\backslash lim\_\{x\; \backslash rightarrow\; 1^\{-\}\}\; \backslash sum\_\{n=0\}^\backslash infty\; a\_n\; x^n$, which is assigned to $f(1)=\backslash sum\_\{n=0\}^\backslash infty\; a\_n$ by the Abel summation method (or A-method).

Origin

• After Norwegian mathematician Niels Henrik Abel (1802-1829).