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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 12, Pages 71–75 (Mi ivm8408)  
Brief communications

Sharp estimates for functions with a pole and a logarithmic singularity

F. G. Avkhadiev

Chair of Function Theory and Approximations, Kazan (Volga Region) Federal University, Kazan, Russia
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Abstract: We consider functions with a pole and a logarithmic singularity. We obtain sharp estimates for the Schwarzian and the Taylor coefficients of the holomorphic part of such functions. We also describe geometric properties of conformal mappings of the exterior of the unit disc with a cut that connects some boundary point with a point at infinity.
Keywords: conformal mappings, Schwarzian, coefficient estimates.
Received: 05.06.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 12, Pages 58–62
DOI: https://doi.org/10.3103/S1066369X11120097
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: F. G. Avkhadiev, “Sharp estimates for functions with a pole and a logarithmic singularity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 12, 71–75; Russian Math. (Iz. VUZ), 55:12 (2011), 58–62
Citation in format AMSBIB
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\by F.~G.~Avkhadiev
\paper Sharp estimates for functions with a~pole and a~logarithmic singularity
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 12
\pages 71--75
\mathnet{http://mi.mathnet.ru/ivm8408}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2963466}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 12
\pages 58--62
\crossref{https://doi.org/10.3103/S1066369X11120097}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856283174}
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