Abel sum
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English[edit]
Etymology[edit]
After Norwegian mathematician Niels Henrik Abel (1802-1829).
Noun[edit]
- (mathematical analysis) Given a power series that is convergent for real x in the open interval (0, 1), the value , which is assigned to by the Abel summation method (or A-method).
- 1967, Jan Mikusiński, Operational Calculus, Cambridge University Press, page 102,
- The Abel sum of is defined as the limit of the corresponding power series:
- .
- 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.
- The Abel sum of is defined as the limit of the corresponding power series:
- 2005, Bulletin of the American Mathematical Society, page 81:
- Jacobi in his Vorlesungen über Dynamik [1884] had used Abel sums to separate variables in the Hamilton-Jacobi equation in connection with the geodesic flow on the surface of a 3-dimensional ellipsoid, etc.
- 2012, Peter L. Duren, Invitation to Classical Analysis, American Mathematical Society, page 180:
- Also, Abel's theorem guarantees that the Abel sum of a convergent series exists and is equal to the ordinary sum.
- 1967, Jan Mikusiński, Operational Calculus, Cambridge University Press, page 102,
Derived terms[edit]
Related terms[edit]
See also[edit]
Further reading[edit]
- Divergent series on Wikipedia.Wikipedia
- Abel's theorem on Wikipedia.Wikipedia
- Abel's summation formula on Wikipedia.Wikipedia