The domain covered by a typically-real function

Author:
A. W. Goodman

Journal:
Proc. Amer. Math. Soc. **64** (1977), 233-237

MSC:
Primary 30A76

DOI:
https://doi.org/10.1090/S0002-9939-1977-0444956-7

MathSciNet review:
0444956

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Abstract: We find the largest possible domain that is covered by for every typically-real function . In the process we obtain a set of universal typically-real functions.

**[1]**D. A. Brannan and W. E. Kirwan,*A covering theorem for typically real functions*, Glasgow Math. J.**10**(1969), 153-155. MR**40**#7431. MR**0254222 (40:7431)****[2]**A. W. Goodman and E. B. Saff,*On univalent functions convex in one direction*(to appear). MR**516461 (80e:30006)****[3]**M. T. McGregor,*On three classes of univalent functions with real coefficients*, J. London Math. Soc.**39**(1964), 43-50. MR**0162931 (29:235)****[4]**M. S. Robertson,*On the coefficients of a typically-real function*, Bull. Amer. Math. Soc.**41**(1935), 565-572. MR**1563142****[5]**W. Rogosinski,*Über positive harmonische Entwicklungen und typisch-reele Potenzreihen*, Math Z.**35**(1932), 93-121. MR**1545292**

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DOI:
https://doi.org/10.1090/S0002-9939-1977-0444956-7

Article copyright:
© Copyright 1977
American Mathematical Society