Let 
be a Bessel function of the first kind,
a Bessel function of the second kind,
and 
the zeros of 
in order of ascending real part. Then for 
and ![R[z]>0](/images/equations/Kneser-SommerfeldFormula/Inline6.svg)
,
![(piJ_nu(xz))/(4J_nu(z))[J_nu(z)N_nu(Xz)-N_nu(z)J_nu(Xz)]=sum_(n=1)^infty(J_nu(j_(nu,n)x)J_nu(j_(nu,n)X))/((z^2-j_(nu,n)^2)J_(nu,n)^('2)(j_(nu,n))).](/images/equations/Kneser-SommerfeldFormula/NumberedEquation1.svg) |
Kneser-Sommerfeld Formula
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.Referenced on Wolfram|Alpha
Kneser-Sommerfeld FormulaCite this as:
Weisstein, Eric W. "Kneser-Sommerfeld Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kneser-SommerfeldFormula.html