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The research of Édouard Goursat’s work on the series \(\sum \frac{A_n}{z-a_n}\) and its influence. (Chinese. English summary) Zbl 1289.01017

Summary: The series \(\sum \frac{A_n}{z-a_n}\) is very important in researching the analytic functions. Édouard Goursat studied this series earlier than others. H. Poincaré, A. Pringsheim and E. Borel studied it under his influences and got some profound results. Based on these researches, E. Borel gave the theories of semi-monogenic functions in particular. This paper analyzes the development and influence of Édouard Goursat’s idea on the basis of reading original sources and of investigating previous researches.

MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
40-03 History of sequences, series, summability

Biographic References:

Goursat, Édouard
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