More on the Bernoulli-Taylor formula for extended umbral calculus (Q860209)

Using the noncomutative \(\psi\)-product \(*_{\psi}\) which is a \(\psi\)-multiplication of functions or formal series with some properties, the author presents the ``\(*_{\psi}\)-Bernoulli-Taylor'' formula with the rest term in the Cauchy form. The product \(*_{\psi}\) is perfectly suitable for the so-called \(\psi\)-extension on Rota's umbral calculus.