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Alpha Function

\begin{figure}\begin{center}\BoxedEPSF{AlphaFunction.epsf}\end{center}\end{figure}


\begin{displaymath}
\alpha_n(z) \equiv \int_1^\infty {t^n e^{-zt} dt} = n! z^{-(n+1)}e^{-z}\sum_{k=0}^n {z^k\over k!}.
\end{displaymath}

The alpha function satisfies the Recurrence Relation

\begin{displaymath}
z\alpha_n(z) = e^{-z}+n\alpha_{n-1}(z).
\end{displaymath}

See also Beta Function (Exponential)




© 1996-9 Eric W. Weisstein
1999-05-25