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The Number of Zeros of a Polynomial in a Half-Plane
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 56:132-147
- Publication Year :
- 1960
- Publisher :
- Cambridge University Press (CUP), 1960.
-
Abstract
- The determination of the number of zeros of a complex polynomial in a half-plane, in particular in the upper and lower, or right and left, half-planes, has been the subject of numerous papers, and a full discussion, with many references, is given in Marden (l) and Wall (2), where the basis for the determination is a continued-fraction expansion, or H.C.F. algorithm, in terms of which the number of zeros in one of the half-planes can be written down at once. In addition, determinantal formulae for the relevant elements of the algorithm can be obtained, and these lead to determinantal criteria for the number of zeros, including that of Hurwitz (3) for the right and left half-planes.
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 56
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi...........bcf121b158fe9d03b890269d8c464e56