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Poisson's Bessel Function Formula


For R[nu]>-1/2,

 J_nu(z)=(z/2)^nu2/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)cos(zcost)sin^(2nu)tdt,

where J_nu(z) is a Bessel function of the first kind, and Gamma(z) is the gamma function.


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References

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

Referenced on Wolfram|Alpha

Poisson's Bessel Function Formula

Cite this as:

Weisstein, Eric W. "Poisson's Bessel Function Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PoissonsBesselFunctionFormula.html

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