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Abel sums

Abel sums is the plural of Abel sum.

Meaning of Abel sum

Noun

Abel sum (plural Abel sums)

  1. Given a power series f(x)=∑ₙ₌₀ ᪲a_nxⁿ that is convergent for real x in the open interval (0, 1), the value lim _(x→1⁻)∑ₙ₌₀ ᪲a_nxⁿ, which is assigned to f(1)=∑ₙ₌₀ ᪲a_n by the Abel summation method (or A-method).
    • lim _(x→1-0)∑ₙ₌₀ ᪲a_nxⁿ.
      The existence of the Abel sum is ascertained when the series in question is known to be summable (C, r) for some value of r.1967, Jan Mikusiński, Operational Calculus, Cambridge University Press, page 102, The Abel sum of ∑a_n is defined as the limit of the corresponding power series

Questions about Abel sums

What is Abel sums the plural of?
Abel sums is the plural of Abel sum.

Words near Abel sums in the dictionary

  1. Abeitas
  2. Abel
  3. Abel polynomial
  4. Abel polynomials
  5. Abel sum
  6. Abel sums
  7. Abel test
  8. Abel tests
  9. Abel's formula
  10. Abel's identity
  11. Abel's impossibility theorem

Source and license

Adapted from Wiktionary: Abel sums (page history and authors); Abel sum (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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