Abel Sum Definition


Given a power series f(x)= \sum_{n=0}^\infty a_n x^n that is convergent for real x in the open interval (0, 1), the value \lim_{x \rightarrow 1^{-}} \sum_{n=0}^\infty a_n x^n, which is assigned to f(1)=\sum_{n=0}^\infty a_n by the Abel summation method (or A-method ).


Origin of Abel Sum

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

    From Wiktionary

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Abel sum