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Borel summability


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1: 1.15 Summability Methods
Abel Summability
Cesàro Summability
Borel Summability
Abel Summability
Cesàro Summability
2: 2.11 Remainder Terms; Stokes Phenomenon
For second-order differential equations, see Olde Daalhuis and Olver (1995a), Olde Daalhuis (1995, 1996), and Murphy and Wood (1997). … The first of these two references also provides an introduction to the powerful Borel transform theory. …
3: 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.
  • 4: Bibliography W
  • A. D. Wheelon (1968) Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.
  • 5: 10.65 Power Series
    For further power series summable in terms of Kelvin functions and their derivatives see Hansen (1975).
    6: Bibliography B
  • J. G. Byatt-Smith (2000) The Borel transform and its use in the summation of asymptotic expansions. Stud. Appl. Math. 105 (2), pp. 83–113.
  • 7: Bibliography S
  • B. Simon (1982) Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.