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Kneser-Sommerfeld Formula

Let $J_\nu(z)$ be a Bessel Function of the First Kind, $N_\nu(z)$ a Neumann Function, and $j_{\nu,n}(z)$the zeros of $z^{-\nu}J_\nu(z)$ in order of ascending Real Part. Then for $0<x<X<1$ and $\Re[z]>0$,

{\pi J_\nu(xz)\over 4J_\nu(z)}[J_\nu(z)N_\nu(Xz)-N_\nu(z)J_\...
..._{\nu,n}X)\over (z^2-{j_{\nu,n}}^2){J'_{\nu,n}}^2(j_{\nu,n})}.


Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.

© 1996-9 Eric W. Weisstein