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Ramanujan's Master Theorem

Suppose that in some Neighborhood of $x=0$,

\begin{displaymath}
F(x)=\sum_{k=0}^\infty {\phi(k)(-x)^k\over k!}.
\end{displaymath}

Then

\begin{displaymath}
\int_0^\infty x^{n-1}F(x)\,dx=\Gamma(n)\phi(-n).
\end{displaymath}


References

Berndt, B. C. Ramanujan's Notebooks: Part I. New York: Springer-Verlag, p. 298, 1985.




© 1996-9 Eric W. Weisstein
1999-05-25