Conformal maps in methods of asymptotic continuation
1987 ◽
Vol 105
(1)
◽
pp. 319-335
Keyword(s):
SynopsisTake the coefficients of a Taylor series expansion of a holomorphic function about its regular point zR. It is known that the holomorphic function possesses an asymptotic expansion about a possibly singular point zs. We show how to construct and calculate the coefficients in the asymptotic expansion from the coefficient of the Taylor series. The main theorem demonstrates that a suitable conformal map is a decisive step in dealing with the problem above. Therefore, a suitable conformal map is critical to a successful summation of divergent series. Some other methods which utilise orthogonal polynomial and Cesaro summability are also discussed. The paper may serve as a theoretical basis for a new computational method.
2005 ◽
Vol 10
(4)
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pp. 333-342
Keyword(s):
1975 ◽
Vol 97
(1)
◽
pp. 45-51
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2011 ◽
Vol 33
(12)
◽
pp. 3299-3310
◽
Keyword(s):