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Hansen-Bessel Formula


J_n(z)=1/(2pi)int_(-pi)^pie^(izcost)e^(in(t-pi/2))dt
(1)
=(i^(-n))/piint_0^pie^(izcost)cos(nt)dt
(2)
=1/piint_0^picos(zsint-nt)dt
(3)

for n=0, 1, 2, ..., where J_n(z) is a Bessel function of the first kind.


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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

Hansen-Bessel Formula

Cite this as:

Weisstein, Eric W. "Hansen-Bessel Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hansen-BesselFormula.html

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