再论推广的Umbral演算的Bernoulli和泰勒公式
More on the Bernoulli and Taylor Formula for Extended Umbral Calculus
摘要：
本文给出了作者最近在所谓的$ψ$ -差分演算的情况下导出的一种新的带有柯西型余项的推广的Bernoulli和泰勒公式，这种差分演算构成了推广的投影演算的典型情况。这类公式的核心重要性是毫无疑问的。最近的出版物确实证实了这一历史经验。它的联系，通过umbrality组合已知至少因为罗塔和穆林源文件，然后到最近延长了许多作者指出，在续集。
英文摘要：
One delivers here the extended Bernoulli and Taylor formula of a new sort with the rest term of the Cauchy type recently derived by the author in the case of the so called $ψ$-difference calculus which constitutes the representative for the purpose case of extended umbral calculus. The central importance of such a type formulas is beyond any doubt. Recent publications do confirm this historically established experience. Its links via umbrality to combinatorics are known at least since Rota and Mullin source papers then up to recently extended by many authors to be indicated in the sequel.
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