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Generalized Function

The class of all regular sequences of Particularly Well-Behaved Functions equivalent to a given regular sequence (sometimes also called a Distribution or Functional). A generalized function $p(x)$ has the properties

\begin{displaymath}
\int_{-\infty}^\infty p'(x)f(x)\,dx=-\int_{-\infty}^\infty p(x)f'(x)\,dx
\end{displaymath}


\begin{displaymath}
\int_{-\infty}^\infty p^{(n)}(x)f(x)\,dx=(-1)^n \int_{-\infty}^\infty p(x)f^{(n)}(x)\,dx.
\end{displaymath}

The Delta Function is a generalized function.

See also Delta Function




© 1996-9 Eric W. Weisstein
1999-05-25