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Schläfli's Formula

For $\Re[z]>0$,


\begin{displaymath}
J_\nu(z)={1\over\pi}\int_0^{\pi/2} \cos(z\sin t-\nu t)\,dt-{\sin(\nu\pi)\over\pi}\int_0^\infty e^{-z\sinh t}e^{-\nu t}\,dt,
\end{displaymath}

where $J_\nu(z)$ is a Bessel Function of the First Kind.


References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1472, 1980.




© 1996-9 Eric W. Weisstein
1999-05-26