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Hello,

Interesting that you pose this question. I am writing an article for the online HP Solve newsletter that discusses a mutli-root finder that locates roots in a range of values. The method can locate roots that are also minima or maxima (something that most root-seeking algorithms fail to do).

Namir

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The functions Bessel function *J*_{n}(z) each have an infinite number of real zeros, all of which are simple with the possible exception of *z = 0*.

For nonnegative *n*, the *k*th **positive** zeros of first kind Bessel functions are denoted *j*_{n,k}, except that *z = 0* is typically counted as the first zero of *J'*_{0}(z)(Abramowitz and Stegun 1972, p. 370).

The first few roots *j*_{n,k} of the Bessel functions are given in the following table for small nonnegative integer values of *n* and *k*.

*k J*_{0}(x) J_{1}(x) J_{2}(x) J_{3}(x) J_{4}(x) J_{5}(x)

1 2.4048 3.8317 5.1356 6.3802 7.5883 8.7715

2 5.5201 7.0156 8.4172 9.7610 11.0647 12.3386

3 8.6537 10.1735 11.6198 13.0152 14.3725 15.7002

4 11.7915 13.3237 14.7960 16.2235 17.6160 18.9801

5 14.9309 16.4706 17.9598 19.4094 20.8269 22.2178

Sources :

http://mathworld.wolfram.com/BesselFunctionZeros.html

http://en.wikipedia.org/wiki/Bessel_function