On Divided Differences.
BASEL UNIV (SWITZERLAND) MATHEMATICS INST
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The report is essentially concerned with four points of the calculus of divided differences. First Hermites integral representation is generalized to the case where the complete set of variables is subdivided into convenient groups. Secondly reasonable general conditions are derived for the existence of the confluent divided differences. This is generalized to the Milne-Thomson representation derived by this author by means of a contour integral in the analytic case. Thirdly the continuity of the divided difference in function of its variables is proved. Finally, the Taylor development of a divided difference is derived.
- Theoretical Mathematics