Some generalizations of the Euler-Knopp transformation
Numerische Mathematik
Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
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We use umbral methods to obtain several general expansion theorems for linear operators and linear functionals. We show in particular that every linear operator admits Newton-type expansions. These expansions are prototypes of numerous classical ones as well as new ones, some of which are powerful enough for use in numerical approximation.