Abel sum

English Etymology After Norwegian mathematician Niels Henrik Abel (1802-1829). Noun en 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. en 2005 Bulletin of the American Mathematical Society https://books.google.com.au/books?id=g_MqAQAAMAAJ&q=%22Abel+sum%22%7C%22Abel+sums%22&dq=%22Abel+sum%22%7C%22Abel+sums%22&hl=en&sa=X&ved=0ahUKEwjRq-_wiv7WAhVIErwKHTCgBakQ6AEI-AIwPw 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. en 2012 Peter L. Duren Invitation to Classical Analysis https://books.google.com.au/books?id=Jyov-EMgbC0C&pg=PA180&dq=%22Abel+sum%22%7C%22Abel+sums%22&hl=en&sa=X&ved=0ahUKEwjRq-_wiv7WAhVIErwKHTCgBakQ6AEIfTAP#v=onepage&q=%22Abel%20sum%22%7C%22Abel%20sums%22&f=false 180 w:American Mathematical Society Also, Abel's theorem guarantees that the Abel sum of a convergent series exists and is equal to the ordinary sum. Derived terms en Abel summable en Abel summation Related terms en Abel mean en Abel summation method See also en summability method en summation method Further reading Divergent series Abel's theorem Abel's summation formula Anagrams en abelmsu bemauls malesub en eponyms