Hartogs-Laurent series

A series

(*)

where and where the are functions holomorphic in some domain which is independent of . If for all , the series (*) is known as a Hartogs series. Any holomorphic function in a Hartogs domain of the type

can be expanded into a Hartogs–Laurent series which converges absolutely and uniformly inside . In complete Hartogs domains this will be the expansion into a Hartogs series. The domains of convergence of Hartogs–Laurent series are domains of the same kind with special and , known as Hartogs radii. If , when all are constant, a Hartogs–Laurent series is called a Laurent series.

References

[1]	V.S. Vladimirov, "Methods of the theory of functions of several complex variables" , M.I.T. (1966) (Translated from Russian)

References

[a1]	H. Behnke, P. Thullen, "Theorie der Funktionen meherer komplexer Veränderlichen" , Springer (1970) (Elraged & Revised Edition. Original: 1934)
[a2]	S. Bochner, W.T. Martin, "Several complex variables" , Princeton Univ. Press (1948)