Banjai, Lehel and Trefethen, Lloyd N. (2001) Numerical solution of the omitted area problem of univalent function theory. Technical Report. Unspecified. (Submitted)
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Abstract
The omitted area problem was posed by Goodman in 1949: what is the maximum area of the unit disk D that can be omitted by the image of the unit disk under a univalent function normalized by f(0)=0 and f'(0)=1? The previous best bounds were 0.240005
<
< .31
. Here the problem is addressed numerically and it is found that these estimates are slightly in error. To ten digits, the correct value appears to be
= 0.2385813248
.
| Item Type: | Technical Report (Technical Report) |
|---|---|
| Subjects: | D - G > Functions of a complex variable H - N > Numerical analysis |
| Research Groups: | Numerical Analysis Group |
| ID Code: | 1228 |
| Deposited By: | Lotti Ekert |
| Deposited On: | 20 May 2011 09:18 |
| Last Modified: | 20 May 2011 09:18 |
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