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Abel summability

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1: 1.15 Summability Methods
Abel Summability
Cesàro Summability
Abel Means
Abel Summability
- f ( t ) d t is Abel summable to L , or …
2: 22.18 Mathematical Applications
§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem
For any two points ( x 1 , y 1 ) and ( x 2 , y 2 ) on this curve, their sum ( x 3 , y 3 ) , always a third point on the curve, is defined by the Jacobi–Abel addition law …a construction due to Abel; see Whittaker and Watson (1927, pp. 442, 496–497). …
3: 2.10 Sums and Sequences
Another version is the Abel–Plana formula: …
  • (c)

    The first infinite integral in (2.10.2) converges.

  • 4: 1.13 Differential Equations
    Then the following relation is known as Abel’s identity
    5: Bibliography F
  • W. B. Ford (1960) Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series. Chelsea Publishing Co., New York.
  • 6: Bibliography W
  • A. D. Wheelon (1968) Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.
  • 7: 10.65 Power Series
    For further power series summable in terms of Kelvin functions and their derivatives see Hansen (1975).
    8: 1.2 Elementary Algebra
    §1.2(iv) Means
    9: Bibliography S
  • B. Simon (1982) Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.
  • 10: Bibliography B
  • H. F. Baker (1995) Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.